We present a solution to the following problem: Does every countable and non-discrete topological (Abelian) group have a countable network with infinite elements? In fact, we show that no maximal topological space allows for a countable network with infinite elements. As a result, we answer the question in the negative. The article also focuses on Malykhin's maximal topological group constructed in 1975 and establishes some unusual properties of countable networks on this special group G. We show, in particular, that for every countable network N for G, the family of finite elements of N is also a network for G.
{"title":"Countable networks on Malykhin's maximal topological group","authors":"Edgar Márquez","doi":"10.4995/agt.2023.18517","DOIUrl":"https://doi.org/10.4995/agt.2023.18517","url":null,"abstract":"We present a solution to the following problem: Does every countable and non-discrete topological (Abelian) group have a countable network with infinite elements? In fact, we show that no maximal topological space allows for a countable network with infinite elements. As a result, we answer the question in the negative. The article also focuses on Malykhin's maximal topological group constructed in 1975 and establishes some unusual properties of countable networks on this special group G. We show, in particular, that for every countable network N for G, the family of finite elements of N is also a network for G.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135893527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Morteza Saheli, Seyed Ali Mohammad Mohsenialhosseini, Hadi Saeidi Goraghani
In this paper, φ-contractions are defined and then, some new fixed point theorems are established for certain nonlinear mappings associated with one-dimensional (c)-comparison functions in fuzzy metric spaces. Next, generalized φ-contractions are defined by using five-dimensional (c)-comparison functions, and the existence of fixed points for nonlinear maps on fuzzy metric spaces is studied. Moreover, some examples are given to illustrate our results.
{"title":"On φ-contractions and fixed point results in fuzzy metric spaces","authors":"Morteza Saheli, Seyed Ali Mohammad Mohsenialhosseini, Hadi Saeidi Goraghani","doi":"10.4995/agt.2023.17130","DOIUrl":"https://doi.org/10.4995/agt.2023.17130","url":null,"abstract":"In this paper, φ-contractions are defined and then, some new fixed point theorems are established for certain nonlinear mappings associated with one-dimensional (c)-comparison functions in fuzzy metric spaces. Next, generalized φ-contractions are defined by using five-dimensional (c)-comparison functions, and the existence of fixed points for nonlinear maps on fuzzy metric spaces is studied. Moreover, some examples are given to illustrate our results.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"10 9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135830374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
G-compactifications of continuous partial actions in the category of limit spaces are considered. In particular, sufficient conditions are given to ensure that (G, X, α) has a largest regular G-compactification.
{"title":"Partial actions on limit spaces","authors":"Bernd Losert, Gary Richardson","doi":"10.4995/agt.2023.18665","DOIUrl":"https://doi.org/10.4995/agt.2023.18665","url":null,"abstract":"G-compactifications of continuous partial actions in the category of limit spaces are considered. In particular, sufficient conditions are given to ensure that (G, X, α) has a largest regular G-compactification.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135893532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let X be a smooth fan and denote its set of endpoints by E(X). Let E be one of the following spaces: the natural numbers, the irrational numbers, or the product of the Cantor set with the natural numbers. We prove that there is a smooth fan X such that E(X) is homeomorphic to E and for every homeomorphism h : X → X , the restriction of h to E(X) is the identity. On the other hand, we also prove that if X is any smooth fan such that E(X) is homeomorphic to complete Erdős space, then X is necessarily homeomorphic to the Lelek fan; this adds to a 1989 result by Włodzimierz Charatonik.
{"title":"Smooth fans that are endpoint rigid","authors":"Rodrigo Hernández-Gutiérrez, Logan C. Hoehn","doi":"10.4995/agt.2023.17922","DOIUrl":"https://doi.org/10.4995/agt.2023.17922","url":null,"abstract":"Let X be a smooth fan and denote its set of endpoints by E(X). Let E be one of the following spaces: the natural numbers, the irrational numbers, or the product of the Cantor set with the natural numbers. We prove that there is a smooth fan X such that E(X) is homeomorphic to E and for every homeomorphism h : X → X , the restriction of h to E(X) is the identity. On the other hand, we also prove that if X is any smooth fan such that E(X) is homeomorphic to complete Erdős space, then X is necessarily homeomorphic to the Lelek fan; this adds to a 1989 result by Włodzimierz Charatonik.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135895242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we prove some fixed point theorems for Lipschitz type mappings in the setting of metric spaces. Our results open up the unexplored area of fixed points of Lipschitz type mappings for investigation.
{"title":"Fixed point of Lipschitz type mappings","authors":"Ravindra K. Bisht","doi":"10.4995/agt.2023.17642","DOIUrl":"https://doi.org/10.4995/agt.2023.17642","url":null,"abstract":"In this paper, we prove some fixed point theorems for Lipschitz type mappings in the setting of metric spaces. Our results open up the unexplored area of fixed points of Lipschitz type mappings for investigation.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135830512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the behavior of some topological and cardinal properties of topological spaces under the influence of the Nτφ -kernel of a space X. It has been proved that the Nτφ-kernel of a space X preserves the density and the network π - weight of normal spaces. Besides, shown that the N-compact kernel of a space X preserves the Souslin properties, the weight, the density, and the π -network weight of normal spaces.
{"title":"Some topological and cardinal properties of the Nτφ-nucleus of a space X","authors":"F. G. Mukhamadiev","doi":"10.4995/agt.2023.17884","DOIUrl":"https://doi.org/10.4995/agt.2023.17884","url":null,"abstract":"In this paper, we study the behavior of some topological and cardinal properties of topological spaces under the influence of the Nτφ -kernel of a space X. It has been proved that the Nτφ-kernel of a space X preserves the density and the network π - weight of normal spaces. Besides, shown that the N-compact kernel of a space X preserves the Souslin properties, the weight, the density, and the π -network weight of normal spaces.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"292 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135893285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Susan Afrooz, Fariborz Azarpanah, Nidaah Hasan Hajee
Whenever the closure of an open set is also open, it is called e-open and if a space have a base consisting of e-open sets, it is called e-space. In this paper we first introduce and study e-spaces and e-continuous functions (we call a function f from a space X to a space Y an e-continuous at x ∈ X if for each open set V containing f(x) there is an e-open set containing x with f ( U ) ⊆ V ). We observe that the quasicomponent of each point in a space X is determined by e-continuous functions on X and it is characterized as the largest set containing the point on which every e-continuous function on X is constant. Next, we study the rings Ce( X ) of all real valued e-continuous functions on a space X. It turns out that Ce( X ) coincides with the ring of real valued clopen continuous functions on X which is a C(Y) for a zero-dimensional space Y whose elements are the quasicomponents of X. Using this fact we characterize the real maximal ideals of Ce( X ) and also give a natural representation of its maximal ideals. Finally we have shown that Ce( X ) determines the topology of X if and only if it is a zero-dimensional space.
{"title":"On e-spaces and rings of real valued e-continuous functions","authors":"Susan Afrooz, Fariborz Azarpanah, Nidaah Hasan Hajee","doi":"10.4995/agt.2023.17743","DOIUrl":"https://doi.org/10.4995/agt.2023.17743","url":null,"abstract":"Whenever the closure of an open set is also open, it is called e-open and if a space have a base consisting of e-open sets, it is called e-space. In this paper we first introduce and study e-spaces and e-continuous functions (we call a function f from a space X to a space Y an e-continuous at x ∈ X if for each open set V containing f(x) there is an e-open set containing x with f ( U ) ⊆ V ). We observe that the quasicomponent of each point in a space X is determined by e-continuous functions on X and it is characterized as the largest set containing the point on which every e-continuous function on X is constant. Next, we study the rings Ce( X ) of all real valued e-continuous functions on a space X. It turns out that Ce( X ) coincides with the ring of real valued clopen continuous functions on X which is a C(Y) for a zero-dimensional space Y whose elements are the quasicomponents of X. Using this fact we characterize the real maximal ideals of Ce( X ) and also give a natural representation of its maximal ideals. Finally we have shown that Ce( X ) determines the topology of X if and only if it is a zero-dimensional space.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135831367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we consider some recent relative versions of Menger property called set strongly star Menger and set star Menger properties and the corresponding Hurewicz-type properties. In particular, using [2], we "easily" prove that the set strong star Menger and set strong star Hurewicz properties are between countable compactness and the property of having countable extent. Also we show that the extent of a regular set star Menger or a set star Hurewicz space cannot exceed c. Moreover, we construct (1) a consistent example of a set star Menger (set star Hurewicz) space which is not set strongly star Menger (set strongly star Hurewicz) and show that (2) the product of a set star Menger (set star Hurewicz) space with a compact space need not be set star Menger (set star Hurewicz). In particular, (1) and (2) answer some questions posed by Kočinac, Konca and Singh in [17] and [23].
{"title":"Some properties defined by relative versions of star-covering properties II","authors":"Maddalena Bonanzinga, Davide Giacopello, Fortunato Maesano","doi":"10.4995/agt.2023.17926","DOIUrl":"https://doi.org/10.4995/agt.2023.17926","url":null,"abstract":"In this paper we consider some recent relative versions of Menger property called set strongly star Menger and set star Menger properties and the corresponding Hurewicz-type properties. In particular, using [2], we \"easily\" prove that the set strong star Menger and set strong star Hurewicz properties are between countable compactness and the property of having countable extent. Also we show that the extent of a regular set star Menger or a set star Hurewicz space cannot exceed c. Moreover, we construct (1) a consistent example of a set star Menger (set star Hurewicz) space which is not set strongly star Menger (set strongly star Hurewicz) and show that (2) the product of a set star Menger (set star Hurewicz) space with a compact space need not be set star Menger (set star Hurewicz). In particular, (1) and (2) answer some questions posed by Kočinac, Konca and Singh in [17] and [23].","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135835608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we investigate shift spaces arising from a multidimensional graph G. In particular, we investigate nonemptiness and existence of periodic points for a multidimensional shift space. We derive sufficient conditions under which these questions can be answered affirmatively. We investigate the structure of the shift space using the generating matrices. We prove that any d-dimensional shift of finite type is finite if and only if it is conjugate to a shift generated through permutation matrices. We prove that if any triangular pattern of the form a b c can be extended to a 1 x 1 square then the two dimensional shift space possesses periodic points. We introduce the notion of an E-pair for a two dimensional shift space. Using the notion of an E-pair, we derive sufficient conditions for non-emptiness of the two dimensional shift space under discussion.
本文研究了由多维图g产生的移动空间，特别是研究了多维移动空间周期点的非空性和存在性。我们推导出这些问题可以被肯定地回答的充分条件。我们利用生成矩阵研究了移位空间的结构。证明任何有限型的d维位移是有限的当且仅当它共轭于由置换矩阵产生的位移。我们证明了如果任何形式为a b c的三角形图形可以扩展到1 x 1的平方，则二维移位空间具有周期点。我们在二维移位空间中引入了e对的概念。利用e对的概念，给出了二维位移空间不空的充分条件。
{"title":"On graph induced symbolic systems","authors":"Prashant Kumar, Puneet Sharma","doi":"10.4995/agt.2023.16662","DOIUrl":"https://doi.org/10.4995/agt.2023.16662","url":null,"abstract":"In this paper, we investigate shift spaces arising from a multidimensional graph G. In particular, we investigate nonemptiness and existence of periodic points for a multidimensional shift space. We derive sufficient conditions under which these questions can be answered affirmatively. We investigate the structure of the shift space using the generating matrices. We prove that any d-dimensional shift of finite type is finite if and only if it is conjugate to a shift generated through permutation matrices. We prove that if any triangular pattern of the form a b c can be extended to a 1 x 1 square then the two dimensional shift space possesses periodic points. We introduce the notion of an E-pair for a two dimensional shift space. Using the notion of an E-pair, we derive sufficient conditions for non-emptiness of the two dimensional shift space under discussion.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135830378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study a property about Polish inverse semigroups similar to the classical theorem of Pettis about Polish groups. In contrast to what happens with Polish groups, not every Polish inverse semigroup have the Pettis property. We present several examples of Polish inverse subsemigroup of the symmetric inverse semigroup I(N) of all partial bijections between subsets of N. We also study whether our examples satisfy automatic continuity.
{"title":"Pettis property for Polish inverse semigroups","authors":"Karen Arana, Jerson Pérez, Carlos Uzcátegui","doi":"10.4995/agt.2023.17396","DOIUrl":"https://doi.org/10.4995/agt.2023.17396","url":null,"abstract":"We study a property about Polish inverse semigroups similar to the classical theorem of Pettis about Polish groups. In contrast to what happens with Polish groups, not every Polish inverse semigroup have the Pettis property. We present several examples of Polish inverse subsemigroup of the symmetric inverse semigroup I(N) of all partial bijections between subsets of N. We also study whether our examples satisfy automatic continuity.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135830381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：