William Chen-Mertens, César Corral-Rojas, Paul J. Szeptycki
We answer questions of Arhangel'skiĭ using spaces defined from combinatorial objects. We first establish further convergence properties of a space constructed from □ ( κ ) showing it is Fréchet-Urysohn for finite sets and a w-space that is not a W-space. We also show that under additional assumptions it may be not bi-sequential, and so providing a consistent example of an absolutely Fréchet α1 space that is not bisequential. In addition, if we do not require the space being α1, we can construct a ZFC example of a countable absolutely Fréchet space that is not bisequential from an almost disjoint family of subsets of the natural numbers.
{"title":"Strong Fréchet properties of spaces constructed from squares and AD families","authors":"William Chen-Mertens, César Corral-Rojas, Paul J. Szeptycki","doi":"10.4995/agt.2023.18504","DOIUrl":"https://doi.org/10.4995/agt.2023.18504","url":null,"abstract":"We answer questions of Arhangel'skiĭ using spaces defined from combinatorial objects. We first establish further convergence properties of a space constructed from □ ( κ ) showing it is Fréchet-Urysohn for finite sets and a w-space that is not a W-space. We also show that under additional assumptions it may be not bi-sequential, and so providing a consistent example of an absolutely Fréchet α1 space that is not bisequential. In addition, if we do not require the space being α1, we can construct a ZFC example of a countable absolutely Fréchet space that is not bisequential from an almost disjoint family of subsets of the natural numbers.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"147 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":"135835480","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 present paper, besides other things, we introduce the concept of Ćirić-generalized contractions via wt−distance and then we will prove some new fixed point results for these mappings, which generalize and improve fixed point theorems by L. B. Ćirić in [9, 8, 10] and also, B. E. Rhoades in [23]. Some examples illustrate usefulness of the new results. At the end, we will give some applications to nonlinear fractional differential equations.
在本文中，我们引入了Ćirić-generalized通过wt -距离收缩的概念，然后证明了这些映射的一些新的不动点结果，这些结果推广和改进了L. B. Ćirić在[9,8,10]和B. E. Rhoades在[23]中的不动点定理。一些例子说明了新结果的实用性。最后，我们将给出非线性分数阶微分方程的一些应用。
{"title":"Ćirić-generalized contraction via wt−distance","authors":"Hosein Lakzian, Darko Kocev, Vladimir Rakočević","doi":"10.4995/agt.2023.19268","DOIUrl":"https://doi.org/10.4995/agt.2023.19268","url":null,"abstract":"In this present paper, besides other things, we introduce the concept of Ćirić-generalized contractions via wt−distance and then we will prove some new fixed point results for these mappings, which generalize and improve fixed point theorems by L. B. Ćirić in [9, 8, 10] and also, B. E. Rhoades in [23]. Some examples illustrate usefulness of the new results. At the end, we will give some applications to nonlinear fractional differential equations.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"19 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":"135893081","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 note, we show that the main result (Theorem 3.2) due to Asim et al. (Appl. Gen. Topol., 23(2), 363-376 (2022) https://doi.org/10.4995/agt.2022.17418) is still valid if we remove the assumption of continuity of the mapping.
在本文中，我们展示了Asim et al. (appll .)的主要结果(定理3.2)。Topol将军。， 23(2)， 363-376 (2022) https://doi.org/10.4995/agt.2022.17418)在去掉映射连续性假设后仍然有效。
{"title":"A note on the fixed point theorem of F-contraction mappings in rectangular M-metric space","authors":"Mujahid Abbas, Rizwan Anjum, Rabia Anwar","doi":"10.4995/agt.2023.18557","DOIUrl":"https://doi.org/10.4995/agt.2023.18557","url":null,"abstract":"In this note, we show that the main result (Theorem 3.2) due to Asim et al. (Appl. Gen. Topol., 23(2), 363-376 (2022) https://doi.org/10.4995/agt.2022.17418) is still valid if we remove the assumption of continuity of the mapping.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"50 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":"135895241","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, the concept of rough representation of a rough topological group on a Banach space is explored. Mainly, the continuity and the irreducibility of rough representations are studied.
本文讨论了Banach空间上粗糙拓扑群的粗糙表示的概念。主要研究粗糙表示的连续性和不可约性。
{"title":"Rough representations of rough topological groups","authors":"Essoyomewè Kieou, Mawoussi Todjro, Yaogan Mensah","doi":"10.4995/agt.2023.18577","DOIUrl":"https://doi.org/10.4995/agt.2023.18577","url":null,"abstract":"In this paper, the concept of rough representation of a rough topological group on a Banach space is explored. Mainly, the continuity and the irreducibility of rough representations are studied.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"28 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":"135894722","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 four new types of contractions called in this order Kannan-type cyclic contraction via interpolation, interpolative Ćirić-Reich-Rus type cyclic contraction, and we prove the existence and uniqueness for a fixed point for each situation.
{"title":"Fixed points results for various types of interpolative cyclic contraction","authors":"Mohamed Edraoui, Amine El koufi, Soukaina Semami","doi":"10.4995/agt.2023.19515","DOIUrl":"https://doi.org/10.4995/agt.2023.19515","url":null,"abstract":"In this paper, we introduce four new types of contractions called in this order Kannan-type cyclic contraction via interpolation, interpolative Ćirić-Reich-Rus type cyclic contraction, and we prove the existence and uniqueness for a fixed point for each situation.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"19 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":"135830239","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 some concepts of ★-(quasi)-pseudometric spaces, and give an example which shows that there is a ★-quasi-pseudometric space which is not a quasi-pseudometric space. We also study the conditions under which ★-quasi-pseudometric semitopological groups are paratopological groups or topological groups.
{"title":"★-quasi-pseudometrics on algebraic structures","authors":"Shi-Yao He, Ying-Ying Jin, Li-Hong Xie","doi":"10.4995/agt.2023.19303","DOIUrl":"https://doi.org/10.4995/agt.2023.19303","url":null,"abstract":"In this paper, we introduce some concepts of ★-(quasi)-pseudometric spaces, and give an example which shows that there is a ★-quasi-pseudometric space which is not a quasi-pseudometric space. We also study the conditions under which ★-quasi-pseudometric semitopological groups are paratopological groups or topological groups.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"147 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":"135893092","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 the existence of fixed point results for set-valued mappings in Menger probabilistic metric spaces equipped with an amorphous binary relation and a Hadžić -type t-norm. For the usability of such findings we present a Kelisky-Rivlin type result for a class of Bernstein type special operators introduced by Deo et. al. [Appl. Math. Comput. 201, (2008), 604-612 ] on the space C([ 0, n/n+1]). In this way, these investigations extend, modify and generalize some prominent recent fixed point results of the existing literature.
{"title":"Fixed points of set-valued mappings in Menger probabilistic metric spaces endowed with an amorphous binary relation","authors":"Gopi Prasad, Sheetal Deshwal, Rupesh K. Srivastav","doi":"10.4995/agt.2023.18993","DOIUrl":"https://doi.org/10.4995/agt.2023.18993","url":null,"abstract":"In this paper, we prove the existence of fixed point results for set-valued mappings in Menger probabilistic metric spaces equipped with an amorphous binary relation and a Hadžić -type t-norm. For the usability of such findings we present a Kelisky-Rivlin type result for a class of Bernstein type special operators introduced by Deo et. al. [Appl. Math. Comput. 201, (2008), 604-612 ] on the space C([ 0, n/n+1]). In this way, these investigations extend, modify and generalize some prominent recent fixed point results of the existing literature.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"14 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":"135835285","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}
This paper continues a series discussing flaws in published assertions concerning fixed points in digital metric spaces.
本文继续讨论一系列关于数字度量空间中不动点的已发表断言的缺陷。
{"title":"Remarks on fixed point assertions in digital topology, 6","authors":"Laurence Boxer","doi":"10.4995/agt.2023.18996","DOIUrl":"https://doi.org/10.4995/agt.2023.18996","url":null,"abstract":"This paper continues a series discussing flaws in published assertions concerning fixed points in digital metric spaces.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"27 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":"135894724","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}
Based on the concept of Cauchy pair Τ-filters, we develop an axiomatic theory of completeness for non-symmetric spaces, such as Τ-quasi-uniform (limit) spaces or L-metric spaces. We show that the category of Τ-quasi-Cauchy spaces is topological and Cartesian closed and we construct a finest completion for a non-complete Τ-quasi-Cauchy space. In the special case of symmetry, Τ-quasi-Cauchy spaces can be identified with Τ-Cauchy spaces.
{"title":"Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion","authors":"G. Jäger","doi":"10.4995/agt.2023.18783","DOIUrl":"https://doi.org/10.4995/agt.2023.18783","url":null,"abstract":"Based on the concept of Cauchy pair Τ-filters, we develop an axiomatic theory of completeness for non-symmetric spaces, such as Τ-quasi-uniform (limit) spaces or L-metric spaces. We show that the category of Τ-quasi-Cauchy spaces is topological and Cartesian closed and we construct a finest completion for a non-complete Τ-quasi-Cauchy space. In the special case of symmetry, Τ-quasi-Cauchy spaces can be identified with Τ-Cauchy spaces.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"4 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76005641","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 investigate the notion of setwise betweenness, a concept introduced by P. Bankston as a generalisation of pointwise betweenness. In the context of continua, we say that a subset C of a continuum X is between distinct points a and b of X if every subcontinuum K of X containing both a and b intersects C. The notion of an interval [a,b] then arises naturally. Further interesting questions are derived from considering such intervals within an associated hyperspace on X. We explore these ideas within the context of the Vietoris topology and n-symmetric product hyperspaces on all nonempty closed subsets of a topological space X, CL(X). Moreover, an alternative pointwise interval, derived from setwise intervals, is introduced.
{"title":"On setwise betweenness","authors":"Q. Shakir","doi":"10.4995/agt.2023.18061","DOIUrl":"https://doi.org/10.4995/agt.2023.18061","url":null,"abstract":"In this article, we investigate the notion of setwise betweenness, a concept introduced by P. Bankston as a generalisation of pointwise betweenness. In the context of continua, we say that a subset C of a continuum X is between distinct points a and b of X if every subcontinuum K of X containing both a and b intersects C. The notion of an interval [a,b] then arises naturally. Further interesting questions are derived from considering such intervals within an associated hyperspace on X. We explore these ideas within the context of the Vietoris topology and n-symmetric product hyperspaces on all nonempty closed subsets of a topological space X, CL(X). Moreover, an alternative pointwise interval, derived from setwise intervals, is introduced.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"15 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84617215","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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