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Applied general topology最新文献

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Sum connectedness in proximity spaces 邻近空间中的和连通性
IF 0.8
Applied general topology Pub Date : 2021-10-01 DOI: 10.4995/agt.2021.14809
Beenu Singh, Davinder Singh
{"title":"Sum connectedness in proximity spaces","authors":"Beenu Singh, Davinder Singh","doi":"10.4995/agt.2021.14809","DOIUrl":"https://doi.org/10.4995/agt.2021.14809","url":null,"abstract":"The notion of sum δ-connected proximity spaces which contain the category of δ-connected and locally δ-connected spaces is defined. Several characterizations of it are substantiated. Weaker forms of sum δ-connectedness are also studied.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"31 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74247850","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}
引用次数: 1
Periodic points of solenoidal automorphisms in terms of inverse limits 逆极限下螺线自同构的周期点
IF 0.8
Applied general topology Pub Date : 2021-10-01 DOI: 10.4995/agt.2021.14589
Sharan Gopal, Faiz Imam
{"title":"Periodic points of solenoidal automorphisms in terms of inverse limits","authors":"Sharan Gopal, Faiz Imam","doi":"10.4995/agt.2021.14589","DOIUrl":"https://doi.org/10.4995/agt.2021.14589","url":null,"abstract":"In this paper, we describe the periodic points of automorphisms of a one dimensional solenoid, considering it as the inverse limit, lim←k (S 1 , γk) of a sequence (γk) of maps on the circle S 1 . The periodic points are discussed for a class of automorphisms on some higher dimensional solenoids also.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"47 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76003679","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}
引用次数: 0
Quantale-valued Cauchy tower spaces and completeness 量子值柯西塔空间与完备性
IF 0.8
Applied general topology Pub Date : 2021-10-01 DOI: 10.4995/agt.2021.15610
G. Jäger, T. Ahsanullah
{"title":"Quantale-valued Cauchy tower spaces and completeness","authors":"G. Jäger, T. Ahsanullah","doi":"10.4995/agt.2021.15610","DOIUrl":"https://doi.org/10.4995/agt.2021.15610","url":null,"abstract":"Generalizing the concept of a probabilistic Cauchy space, we introduce quantale-valued Cauchy tower spaces. These spaces encompass quantale-valued metric spaces, quantale-valued uniform (convergence) tower spaces and quantale-valued convergence tower groups. For special choices of the quantale, classical and probabilistic metric spaces are covered and probabilistic and approach Cauchy spaces arise. We also study completeness and completion in this setting and establish a connection to the Cauchy completeness of a quantale-valued metric space.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"11 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74382256","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}
引用次数: 0
Geometrical properties of the space of idempotent probability measures 幂等概率测度空间的几何性质
IF 0.8
Applied general topology Pub Date : 2021-10-01 DOI: 10.4995/agt.2021.15101
Kholsaid Kholturayev
{"title":"Geometrical properties of the space of idempotent probability measures","authors":"Kholsaid Kholturayev","doi":"10.4995/agt.2021.15101","DOIUrl":"https://doi.org/10.4995/agt.2021.15101","url":null,"abstract":"Although traditional and idempotent mathematics are \"parallel'', by an application of the category theory we show that objects obtained the similar rules over traditional and idempotent mathematics must not be \"parallel''. At first we establish for a compact metric space X the spaces P(X) of probability measures and I(X) idempotent probability measures are homeomorphic (\"parallelism''). Then we construct an example which shows that the constructions P and I form distinguished functors from each other (\"parallelism'' negation). Further for a compact Hausdorff space X we establish that the hereditary normality of I3(X) X implies the metrizability of X.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"8 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82670942","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}
引用次数: 5
On a probabilistic version of Meir-Keeler type fixed point theorem for a family of discontinuous operators 不连续算子族的Meir-Keeler不动点定理的一个概率版本
IF 0.8
Applied general topology Pub Date : 2021-10-01 DOI: 10.4995/agt.2021.15561
R. Bisht, V. Rakočević
{"title":"On a probabilistic version of Meir-Keeler type fixed point theorem for a family of discontinuous operators","authors":"R. Bisht, V. Rakočević","doi":"10.4995/agt.2021.15561","DOIUrl":"https://doi.org/10.4995/agt.2021.15561","url":null,"abstract":"A Meir-Keeler type fixed point theorem for a family of mappings is proved in Menger probabilistic metric space (Menger PM-space). We establish that completeness of the space is equivalent to fixed point property for a larger class of mappings that includes continuous as well as discontinuous mappings. In addition to it, a probabilistic fixed point theorem satisfying (ϵ - δ) type non-expansive mappings is established.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"24 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90803612","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}
引用次数: 1
Disconnection in the Alexandroff duplicate 亚历山德罗夫副本的断线
IF 0.8
Applied general topology Pub Date : 2021-10-01 DOI: 10.4995/agt.2021.14602
Papiya Bhattacharjee, Michelle L. Knox, W. W. McGovern
{"title":"Disconnection in the Alexandroff duplicate","authors":"Papiya Bhattacharjee, Michelle L. Knox, W. W. McGovern","doi":"10.4995/agt.2021.14602","DOIUrl":"https://doi.org/10.4995/agt.2021.14602","url":null,"abstract":"It was demonstrated in [2] that the Alexandroff duplicate of the Čech-Stone compactification of the naturals is not extremally disconnected. The question was raised as to whether the Alexandroff duplicate of a non-discrete extremally disconnected space can ever be extremally disconnected. We answer this question in the affirmative; an example of van Douwen is significant. In a slightly different direction we also characterize when the Alexandroff duplicate of a space is a P-space as well as when it is an almost P-space.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"8 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75677782","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}
引用次数: 2
Lipschitz integral operators represented by vector measures 由向量测度表示的Lipschitz积分算子
IF 0.8
Applied general topology Pub Date : 2021-10-01 DOI: 10.4995/agt.2021.15061
E. Dahia, Khaled Hamidi
{"title":"Lipschitz integral operators represented by vector measures","authors":"E. Dahia, Khaled Hamidi","doi":"10.4995/agt.2021.15061","DOIUrl":"https://doi.org/10.4995/agt.2021.15061","url":null,"abstract":"In this paper we introduce the concept of Lipschitz Pietsch-p-integral mappings, (1≤p≤∞), between a metric space and a Banach space. We represent these mappings by an integral with respect to a vectormeasure defined on a suitable compact Hausdorff space, obtaining in this way a rich factorization theory through the classical Banach spaces C(K), L_p(μ,K) and L_∞(μ,K). Also we show that this type of operators fits in the theory of composition Banach Lipschitz operator ideals. For p=∞, we characterize the Lipschitz Pietsch-∞-integral mappings by a factorization schema through a weakly compact operator. Finally, the relationship between these mappings and some well known Lipschitz operators is given.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"76 6","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72632906","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}
引用次数: 0
The periodic points of ε-contractive maps in fuzzy metric spaces 模糊度量空间中ε-压缩映射的周期点
IF 0.8
Applied general topology Pub Date : 2021-10-01 DOI: 10.4995/agt.2021.14449
T. Sun, Caihong Han, G. Su, Bin Qin, Lue Li
{"title":"The periodic points of ε-contractive maps in fuzzy metric spaces","authors":"T. Sun, Caihong Han, G. Su, Bin Qin, Lue Li","doi":"10.4995/agt.2021.14449","DOIUrl":"https://doi.org/10.4995/agt.2021.14449","url":null,"abstract":"In this paper, we introduce the notion of ε-contractive maps in fuzzy metric space (X, M, ∗) and study the periodicities of ε-contractive maps. We show that if (X, M, ∗) is compact and f : X −→ X is ε-contractive, then P(f) = ∩ ∞n=1f n (X) and each connected component of X contains at most one periodic point of f, where P(f) is the set of periodic points of f. Furthermore, we present two examples to illustrate the applicability of the obtained results.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88365162","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}
引用次数: 0
Orbitally discrete coarse spaces 轨道离散的粗空间
IF 0.8
Applied general topology Pub Date : 2021-10-01 DOI: 10.4995/agt.2021.13874
I. Protasov
{"title":"Orbitally discrete coarse spaces","authors":"I. Protasov","doi":"10.4995/agt.2021.13874","DOIUrl":"https://doi.org/10.4995/agt.2021.13874","url":null,"abstract":"Given a coarse space (X, E), we endow X with the discrete topology and denote X ♯ = {p ∈ βG : each member P ∈ p is unbounded }. For p, q ∈ X ♯ , p||q means that there exists an entourage E ∈ E such that E[P] ∈ q for each P ∈ p. We say that (X, E) is orbitally discrete if, for every p ∈ X ♯ , the orbit p = {q ∈ X ♯ : p||q} is discrete in βG. We prove that every orbitally discrete space is almost finitary and scattered.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"29 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84672225","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}
引用次数: 0
Further aspects of I K-convergence in topological spaces 拓扑空间中I - k收敛的进一步方面
IF 0.8
Applied general topology Pub Date : 2021-10-01 DOI: 10.4995/agt.2021.14868
Ankur Sharmah, D. Hazarika
{"title":"Further aspects of I K-convergence in topological spaces","authors":"Ankur Sharmah, D. Hazarika","doi":"10.4995/agt.2021.14868","DOIUrl":"https://doi.org/10.4995/agt.2021.14868","url":null,"abstract":"In this paper, we obtain some results on the relationships between different ideal convergence modes namely, I K, I K∗ , I, K, I ∪ K and (I ∪K) ∗ . We introduce a topological space namely I K-sequential space and show that the class of I K-sequential spaces contain the sequential spaces. Further I K-notions of cluster points and limit points of a function are also introduced here. For a given sequence in a topological space X, we characterize the set of I K-cluster points of the sequence as closed subsets of X.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"5 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81893095","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}
引用次数: 2
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