In the present paper we introduce a generalization of the complete invariance property (CIP) for metric spaces, which we will call the ε-approximated complete invariance property (ε-ACIP). For our goals, we will use the so called degree of nondensifiability (DND) which, roughly speaking, measures (in the specified sense) the distance from a bounded metric space to its class of Peano continua. Our main result relates the ε-ACIP with the DND and, in particular, proves that a densifiable metric space has the ε-ACIP for each ε>0. Also, some essentials differences between the CIP and the ε-ACIP are shown.
{"title":"The ε-approximated complete invariance property","authors":"G. García","doi":"10.4995/agt.2022.16641","DOIUrl":"https://doi.org/10.4995/agt.2022.16641","url":null,"abstract":"In the present paper we introduce a generalization of the complete invariance property (CIP) for metric spaces, which we will call the ε-approximated complete invariance property (ε-ACIP). For our goals, we will use the so called degree of nondensifiability (DND) which, roughly speaking, measures (in the specified sense) the distance from a bounded metric space to its class of Peano continua. Our main result relates the ε-ACIP with the DND and, in particular, proves that a densifiable metric space has the ε-ACIP for each ε>0. Also, some essentials differences between the CIP and the ε-ACIP are shown.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"65 3 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82981995","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}
Dalila Boureni, S. Georgiev, A. Kheloufi, K. Mebarki
In this article we study a class of Euler equations of compressible fluid dynamics. We give conditions under which the considered equations have at least one and at least two classical solutions. To prove our main results we propose a new approach based upon recent theoretical results.
{"title":"Classical solutions for the Euler equations of compressible fluid dynamics: A new topological approach","authors":"Dalila Boureni, S. Georgiev, A. Kheloufi, K. Mebarki","doi":"10.4995/agt.2022.15963","DOIUrl":"https://doi.org/10.4995/agt.2022.15963","url":null,"abstract":"In this article we study a class of Euler equations of compressible fluid dynamics. We give conditions under which the considered equations have at least one and at least two classical solutions. To prove our main results we propose a new approach based upon recent theoretical results.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"12 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90760979","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}
A space X is said to be set star-Lindelöf if for each nonempty subset A of X and each collection U of open sets in X such that A ⊆⋃U, there is a countable subset V of U such that A ⊆ St (⋃V,U). The class of set star-Lindelöf spaces lie between the class of Lindel öf spaces and the class of star-Lindelöf spaces. In this paper, we investigate the relationship between set star-Lindelöf spaces and other related spaces by providing some suitable examples and study the topological properties of set star-Lindelöf spaces.
{"title":"On set star-Lindelöf spaces","authors":"Sumit Singh","doi":"10.4995/agt.2022.17021","DOIUrl":"https://doi.org/10.4995/agt.2022.17021","url":null,"abstract":"A space X is said to be set star-Lindelöf if for each nonempty subset A of X and each collection U of open sets in X such that A ⊆⋃U, there is a countable subset V of U such that A ⊆ St (⋃V,U). The class of set star-Lindelöf spaces lie between the class of Lindel öf spaces and the class of star-Lindelöf spaces. In this paper, we investigate the relationship between set star-Lindelöf spaces and other related spaces by providing some suitable examples and study the topological properties of set star-Lindelöf spaces.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"523 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72418530","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 topological spaces X and Y, let Qp(X,Y) be the space of all quasicontinuous functions from X to Y with the topology of pointwise convergence. In this paper, we study the cardinal invariants such as cellularity, character, weight, density, pseudocharacter and spread of the space Qp(X,Y). We also discuss the properties of the restriction and induced maps related to the space Qp(X,Y).
{"title":"Cardinal invariants and special maps of quasicontinuous functions with the topology of pointwise convergence","authors":"Mandeep Kumar, B. Tyagi","doi":"10.4995/agt.2022.16925","DOIUrl":"https://doi.org/10.4995/agt.2022.16925","url":null,"abstract":"For topological spaces X and Y, let Qp(X,Y) be the space of all quasicontinuous functions from X to Y with the topology of pointwise convergence. In this paper, we study the cardinal invariants such as cellularity, character, weight, density, pseudocharacter and spread of the space Qp(X,Y). We also discuss the properties of the restriction and induced maps related to the space Qp(X,Y).","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"188 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83052756","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 a fixed point result for F- contraction principle in the framework of rectangular M-metric space. An example is also adopted to exhibit the utility of our result. Finally, we apply our fixed point result to show the existence of solution of Fredholm integral equation.
{"title":"Fixed point theorems for F- contraction mapping in complete rectangular M-metric space","authors":"Mohammad Asim, Samad Mujahid, I. Uddin","doi":"10.4995/agt.2022.17418","DOIUrl":"https://doi.org/10.4995/agt.2022.17418","url":null,"abstract":"In this paper, we prove a fixed point result for F- contraction principle in the framework of rectangular M-metric space. An example is also adopted to exhibit the utility of our result. Finally, we apply our fixed point result to show the existence of solution of Fredholm integral equation.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"42 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73343786","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 present new results regarding S2-paracompactness, that we estab-lished in [1], and its relation with other properties such as S-normality, epinormality and L-paracompactness.
{"title":"Results about S2-paracompactness","authors":"Ohud Alghamdi, Lutfi Kalantan","doi":"10.4995/agt.2022.17006","DOIUrl":"https://doi.org/10.4995/agt.2022.17006","url":null,"abstract":"We present new results regarding S2-paracompactness, that we estab-lished in [1], and its relation with other properties such as S-normality, epinormality and L-paracompactness.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"30 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89373548","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 paper is to introduce the class of enriched interpolative Kannan type operators on Banach space that contains theclasses of enriched Kannan operators, interpolative Kannan type contraction operators and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. A convergence theorem for the Krasnoselskij iteration method to approximate fixed point of the enriched interpolative Kannan type operators is proved. We study well-posedness, Ulam-Hyers stability and periodic point property of operators introduced herein. As an application of the main result, variational inequality problems is solved.
{"title":"Fixed point results of enriched interpolative Kannan type operators with applications","authors":"M. Abbas, Rizwana Anjum, Shakeela Riasat","doi":"10.4995/agt.2022.16701","DOIUrl":"https://doi.org/10.4995/agt.2022.16701","url":null,"abstract":"The purpose of this paper is to introduce the class of enriched interpolative Kannan type operators on Banach space that contains theclasses of enriched Kannan operators, interpolative Kannan type contraction operators and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. A convergence theorem for the Krasnoselskij iteration method to approximate fixed point of the enriched interpolative Kannan type operators is proved. We study well-posedness, Ulam-Hyers stability and periodic point property of operators introduced herein. As an application of the main result, variational inequality problems is solved.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77299963","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}
One of the fundamental problem in rings of continuous function is to extract those spaces for which C(X) determines X, that is to investigate X and Y such that C(X) isomorphic with C(Y ) implies X homeomorphic with Y. The development started back from Tychonoff who first pointed out inevitability of Tychonoff space in this category of problem. Later S. Banach and M. Stone proved independently with slight variance, that if X is compact Hausdorff space, C(X) also determine X. Their works were maximally extended by E. Hewitt by introducing realcompact spaces and later Melvin Henriksen and Biswajit Mitra solved the problem for locally compact and nearly realcompact spaces. In this paper we tried to develop an inherent theory of this problem to cover up all the works in the literature introducing a notion so called P-compact spaces.
{"title":"C(X) determines X - an inherent theory","authors":"B. Mitra, Sanjib Das","doi":"10.4995/agt.2023.17569","DOIUrl":"https://doi.org/10.4995/agt.2023.17569","url":null,"abstract":"One of the fundamental problem in rings of continuous function is to extract those spaces for which C(X) determines X, that is to investigate X and Y such that C(X) isomorphic with C(Y ) implies X homeomorphic with Y. The development started back from Tychonoff who first pointed out inevitability of Tychonoff space in this category of problem. Later S. Banach and M. Stone proved independently with slight variance, that if X is compact Hausdorff space, C(X) also determine X. Their works were maximally extended by E. Hewitt by introducing realcompact spaces and later Melvin Henriksen and Biswajit Mitra solved the problem for locally compact and nearly realcompact spaces. In this paper we tried to develop an inherent theory of this problem to cover up all the works in the literature introducing a notion so called P-compact spaces.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80043680","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 define uniformities and topologies as relators and show the equivalences of these definitions with the classical ones. For this, we summarize the essential properties of relators, using their theory from earlier works of Á. Száz.Moreover, we prove implications between important topological properties of relators and disprove others. Finally, we show that our earlier analogous definition [G. Pataki, Investigation of proximal spaces using relators, Axioms 10, no. 3 (2021): 143.] for uniformly and proximally filtered property is equivalent to the topological one.At the end of this paper, uniformities and topologies are defined in the same way. This will give us new possibilities to compare these and other topological structures.
{"title":"Investigation of topological spaces using relators","authors":"G. Pataki","doi":"10.4995/agt.2022.16128","DOIUrl":"https://doi.org/10.4995/agt.2022.16128","url":null,"abstract":"In this paper, we define uniformities and topologies as relators and show the equivalences of these definitions with the classical ones. For this, we summarize the essential properties of relators, using their theory from earlier works of Á. Száz.Moreover, we prove implications between important topological properties of relators and disprove others. Finally, we show that our earlier analogous definition [G. Pataki, Investigation of proximal spaces using relators, Axioms 10, no. 3 (2021): 143.] for uniformly and proximally filtered property is equivalent to the topological one.At the end of this paper, uniformities and topologies are defined in the same way. This will give us new possibilities to compare these and other topological structures.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"4 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75669171","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}
Krasner hyperring is one of the generalizations of the classical ring in literature. In this paper, the notion of topological Krasner hyperring is introduced as a generalization of topological ring and variant of isomorphism theorems are studied
{"title":"Topological Krasner hyperrings with special emphasis on isomorphism theorems","authors":"Manooranjan Singha, Kousik Das","doi":"10.4995/agt.2022.14778","DOIUrl":"https://doi.org/10.4995/agt.2022.14778","url":null,"abstract":"Krasner hyperring is one of the generalizations of the classical ring in literature. In this paper, the notion of topological Krasner hyperring is introduced as a generalization of topological ring and variant of isomorphism theorems are studied","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82016619","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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