L. Kočinac, F. Mukhamadiev, A. Sadullaev, Sh. U. Meyliev
In this paper the network-type properties (network,cs−network,cs∗−network,cn−network andck−network) of the spaceSPnGXofG-permutation degree ofXare studied. It is proved that:(1) IfXis aT1-space that has a network of cardinality≤κ, thenSPnGXhas a network of cardinality≤κ;(2) IfXis aT1-space that has acs-network (resp.cs∗-network) ofcardinality≤κ, thenSPnGXhas acs-network (resp.cs∗-network) ofcardinality≤κ;(3) IfXis aT1-space that has acn-network (resp.ck-network) ofcardinality≤κ, thenSPnGXhas acn-network (resp.ck−network) ofcardinality≤κ.
{"title":"Some network-type properties of the space of G-permutation degree","authors":"L. Kočinac, F. Mukhamadiev, A. Sadullaev, Sh. U. Meyliev","doi":"10.4995/agt.2023.18985","DOIUrl":"https://doi.org/10.4995/agt.2023.18985","url":null,"abstract":"In this paper the network-type properties (network,cs−network,cs∗−network,cn−network andck−network) of the spaceSPnGXofG-permutation degree ofXare studied. It is proved that:(1) IfXis aT1-space that has a network of cardinality≤κ, thenSPnGXhas a network of cardinality≤κ;(2) IfXis aT1-space that has acs-network (resp.cs∗-network) ofcardinality≤κ, thenSPnGXhas acs-network (resp.cs∗-network) ofcardinality≤κ;(3) IfXis aT1-space that has acn-network (resp.ck-network) ofcardinality≤κ, thenSPnGXhas acn-network (resp.ck−network) ofcardinality≤κ.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"78 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77021817","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}
For a Tychonoff space X, the lattice UX was introduced in L. A. Pérez-Morales, G. Delgadillo-Piñón, and R. Pichardo-Mendoza, The lattice of uniform topologies on C(X), Questions and Answers in General Topology 39 (2021), 65-71. In the present paper we continue the study of UX. To be specific, the present paper deals, in its first half, with structural and categorical properties of UX, while in its second part focuses on cardinal characteristics of the lattice and how these relate to some cardinal functions of the space X.
对于Tychonoff空间X，引入了格UX, L. a . psamrez - morales, G. Delgadillo-Piñón, R. Pichardo-Mendoza, C(X)上一致拓扑的格，一般拓扑问答39(2021)，65-71。在本文中，我们继续对用户体验进行研究。具体而言，本文在其前半部分涉及UX的结构和分类属性，而在其第二部分侧重于晶格的基本特征以及这些特征如何与空间X的一些基本函数相关。
{"title":"New results regarding the lattice of uniform topologies on C(X)","authors":"Roberto Pichardo-Mendoza, Alejandro R'ios-Herrej'on","doi":"10.4995/agt.2023.18738","DOIUrl":"https://doi.org/10.4995/agt.2023.18738","url":null,"abstract":"For a Tychonoff space X, the lattice UX was introduced in L. A. Pérez-Morales, G. Delgadillo-Piñón, and R. Pichardo-Mendoza, The lattice of uniform topologies on C(X), Questions and Answers in General Topology 39 (2021), 65-71.\u0000In the present paper we continue the study of UX. To be specific, the present paper deals, in its first half, with structural and categorical properties of UX, while in its second part focuses on cardinal characteristics of the lattice and how these relate to some cardinal functions of the space X.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85190520","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 consider a new class of nonlinear mappings that generalizes two well-known classes of nonexpansive type mappings and extends some other classes of mappings. We present some existence and convergence results for this class of mappings. Some illustrative examples presented herein show the generality of the obtained results.
{"title":"Fixed point theorems for a new class of nonexpansive mappings","authors":"R. Pant, Rahul Shukla","doi":"10.4995/agt.2022.17359","DOIUrl":"https://doi.org/10.4995/agt.2022.17359","url":null,"abstract":"We consider a new class of nonlinear mappings that generalizes two well-known classes of nonexpansive type mappings and extends some other classes of mappings. We present some existence and convergence results for this class of mappings. Some illustrative examples presented herein show the generality of the obtained results.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90140299","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 introduce the notion of C*-algebra valued quasi metric space to generalize the notion of C*-algebra valued metric space and investigate the topological properties besides proving some core fixed point results. Finally, we employ our one of the main results to examine the existence and uniqueness of the solution for a system of Fredholm integral equations.
{"title":"C*-algebra valued quasi metric spaces and fixed point results with an application","authors":"Mohammad Asim, Santosh Kumar, M. Imdad, R. George","doi":"10.4995/agt.2022.16783","DOIUrl":"https://doi.org/10.4995/agt.2022.16783","url":null,"abstract":"In this paper, we introduce the notion of C*-algebra valued quasi metric space to generalize the notion of C*-algebra valued metric space and investigate the topological properties besides proving some core fixed point results. Finally, we employ our one of the main results to examine the existence and uniqueness of the solution for a system of Fredholm integral equations.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"52 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86842988","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 metric continuum and n a positive integer. Let Fn (X) be the hyperspace of nonempty subsets of X with at most n points. If 0 < m < n, we consider the quotient space Fnm (X) = Fn (X)/Fm (X). Given a mapping f from X into X, we consider the induced mappings fn from Fn (X) into Fn (X) and fnm from Fnm (X) into Fnm (X). In this paper we study the relations among the dynamics of the mappings f, fn, and fnm and we answer some questions, by F. Barragán, A. Santiago-Santos and J. Tenorio, related to the properties: minimality, irreducibility, strong transitive and turbulence.
设X是度规连续统n是正整数。设Fn (X)是X的非空子集的超空间，它最多有n个点。如果0 < m < n,我们考虑到危机的商空间(X) = Fn (X) / Fm (X)给定一个映射f从X到X,我们认为诱导映射Fn Fn (X)为Fn (X)和危机的危机(X)等(X)在本文中,我们研究之间的关系的动态映射f, Fn,等于是我们回答一些问题,通过f·巴拉,a . Santiago-Santos和j . Tenorio相关属性:极小性,不可约性,强大的传递和动荡。
{"title":"Dynamics of induced mappings on symmetric products, some answers","authors":"A. Illanes, V. Martínez-de-la-Vega","doi":"10.4995/agt.2022.17492","DOIUrl":"https://doi.org/10.4995/agt.2022.17492","url":null,"abstract":"Let X be a metric continuum and n a positive integer. Let Fn (X) be the hyperspace of nonempty subsets of X with at most n points. If 0 < m < n, we consider the quotient space Fnm (X) = Fn (X)/Fm (X). Given a mapping f from X into X, we consider the induced mappings fn from Fn (X) into Fn (X) and fnm from Fnm (X) into Fnm (X). In this paper we study the relations among the dynamics of the mappings f, fn, and fnm and we answer some questions, by F. Barragán, A. Santiago-Santos and J. Tenorio, related to the properties: minimality, irreducibility, strong transitive and turbulence.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82448034","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 present a new class of cyclic (noncyclic) α-ψ and β-ψ condensing operators and survey the existence of best proximity points (pairs) as well as coupled best proximity points (pairs) in the setting of reflexive Busemann convex spaces. Then an application of the main existence result to study the existence of an optimal solution for a system of differential equations is demonstrated.
{"title":"Best proximity point (pair) results via MNC in Busemann convex metric spaces","authors":"M. Gabeleh, P. Patle","doi":"10.4995/agt.2022.14000","DOIUrl":"https://doi.org/10.4995/agt.2022.14000","url":null,"abstract":"In this paper, we present a new class of cyclic (noncyclic) α-ψ and β-ψ condensing operators and survey the existence of best proximity points (pairs) as well as coupled best proximity points (pairs) in the setting of reflexive Busemann convex spaces. Then an application of the main existence result to study the existence of an optimal solution for a system of differential equations is demonstrated.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"43 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87873024","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}
Using the concept of m-open sets, M-regularity and M-normality are introduced and investigated. Both these notions are closed under arbitrary product. M-normal spaces are found to satisfy a result similar to Urysohn lemma. It is shown that closed sets can be separated by m-continuous functions in a regular space.
{"title":"A Urysohn lemma for regular spaces","authors":"Ankit Gupta, R. D. Sarma","doi":"10.4995/agt.2022.16720","DOIUrl":"https://doi.org/10.4995/agt.2022.16720","url":null,"abstract":"Using the concept of m-open sets, M-regularity and M-normality are introduced and investigated. Both these notions are closed under arbitrary product. M-normal spaces are found to satisfy a result similar to Urysohn lemma. It is shown that closed sets can be separated by m-continuous functions in a regular space.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"45 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79742411","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 R be a commutative ring with identity and M a unitary R-module. The fuzzy classical primary spectrum F cp.spec(M) is the collection of all fuzzy classical primary submodules A of M, the recent generalization of fuzzy primary ideals and fuzzy classical prime submodules. In this paper, we topologize FM(M) with a topology having the fuzzy primary Zariski topology on the fuzzy classical primary spectrum F cp.spec(M) as a subspace topology, and investigate the properties of this topological space.
{"title":"Zariski topology on the spectrum of fuzzy classical primary submodules","authors":"P. Panpho, P. Yiarayong","doi":"10.4995/agt.2022.17427","DOIUrl":"https://doi.org/10.4995/agt.2022.17427","url":null,"abstract":"Let R be a commutative ring with identity and M a unitary R-module. The fuzzy classical primary spectrum F cp.spec(M) is the collection of all fuzzy classical primary submodules A of M, the recent generalization of fuzzy primary ideals and fuzzy classical prime submodules. In this paper, we topologize FM(M) with a topology having the fuzzy primary Zariski topology on the fuzzy classical primary spectrum F cp.spec(M) as a subspace topology, and investigate the properties of this topological space.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"20 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73843635","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 article, we prove that the group of all increasing homeomorphisms on R has exactly five normal subgroups, and the group of all homeomorphisms on R has exactly four normal subgroups. There are several results known about the group of homeomorphisms on R and about the group of increasing homeomorphisms on R ([2], [6], [7] and [8]), but beyond this there is virtually nothing in the literature concerning the topological structure in the aspects of topological dynamics. In this paper, we analyze this structure in some detail.
{"title":"On the group of homeomorphisms on R: A revisit","authors":"K. Ali Akbar, T. Mubeena","doi":"10.4995/agt.2022.16143","DOIUrl":"https://doi.org/10.4995/agt.2022.16143","url":null,"abstract":" In this article, we prove that the group of all increasing homeomorphisms on R has exactly five normal subgroups, and the group of all homeomorphisms on R has exactly four normal subgroups. There are several results known about the group of homeomorphisms on R and about the group of increasing homeomorphisms on R ([2], [6], [7] and [8]), but beyond this there is virtually nothing in the literature concerning the topological structure in the aspects of topological dynamics. In this paper, we analyze this structure in some detail.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"23 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86682869","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}
The purpose of this article is to identify the largest subring of the ring of all real valued functions on a Tychonoff space X, which forms a topological ring endowed with the m-topology.
{"title":"The largest topological ring of functions endowed with the m-topology","authors":"T. Chauhan, V. Jindal","doi":"10.4995/agt.2022.17080","DOIUrl":"https://doi.org/10.4995/agt.2022.17080","url":null,"abstract":"The purpose of this article is to identify the largest subring of the ring of all real valued functions on a Tychonoff space X, which forms a topological ring endowed with the m-topology.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"1983 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82212457","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}
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