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Uniformly refinable maps 均匀可细化映射
IF 0.8
Applied general topology Pub Date : 2023-04-05 DOI: 10.4995/agt.2023.17345
S. Macías
{"title":"Uniformly refinable maps","authors":"S. Macías","doi":"10.4995/agt.2023.17345","DOIUrl":"https://doi.org/10.4995/agt.2023.17345","url":null,"abstract":"We introduce the notion of uniformly refinable map for compact, Hausdorff spaces, as a generalization of refinable maps originallydefined for metric continua by Jo Ford (Heath) and Jack W. Rogers, Jr., Refinable maps, Colloq. Math., 39 (1978), 263-269.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"40 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85033905","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
Common fixed point results for a generalized ( ψ, φ )-rational contraction 广义(ψ， φ)-有理收缩的公共不动点结果
IF 0.8
Applied general topology Pub Date : 2023-04-05 DOI: 10.4995/agt.2023.18320
M. Arya, N. Chandra, M. Joshi
{"title":"Common fixed point results for a generalized ( ψ, φ )-rational contraction","authors":"M. Arya, N. Chandra, M. Joshi","doi":"10.4995/agt.2023.18320","DOIUrl":"https://doi.org/10.4995/agt.2023.18320","url":null,"abstract":"In this paper, we obtain two common fixed point results for mappings satisfying the generalized (ψ,φ)-contractive type conditions given by a rational expression on a complete metric space.  Our results generalize several well known theorems of the literature in the context of (ψ,φ)-rational contraction. In addition, there is an example for obtained results.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"76 6 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83468871","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
Selection principles and bitopological hyperspaces 选择原则和双拓扑超空间
IF 0.8
Applied general topology Pub Date : 2023-04-05 DOI: 10.4995/agt.2023.12424
A. Osipov
{"title":"Selection principles and bitopological hyperspaces","authors":"A. Osipov","doi":"10.4995/agt.2023.12424","DOIUrl":"https://doi.org/10.4995/agt.2023.12424","url":null,"abstract":"In this paper we continue to research relationships between closure-type properties of hyperspaces over a space X and covering properties of X. For a Hausdorff space X we denote by 2X the family of all closed subsets of X. We investigate selection properties of the bitopological space (2X, Δ1+ , Δ2+) where Δi+ is the upper Δi-topology for each i=1,2.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"61 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78898464","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
Interpolative contractions and discontinuity at fixed point 不动点处的插值收缩和不连续
IF 0.8
Applied general topology Pub Date : 2023-04-05 DOI: 10.4995/agt.2023.18552
N. Taş
{"title":"Interpolative contractions and discontinuity at fixed point","authors":"N. Taş","doi":"10.4995/agt.2023.18552","DOIUrl":"https://doi.org/10.4995/agt.2023.18552","url":null,"abstract":"In this paper, we investigate new solutions to the Rhoades' discontinuity problem on the existence of a self-mapping which has a fixed point but is not continuous at the fixed point on metric spaces. To do this, we use the number defined as n(x,y)=[d(x,y)]β[d(x,Ty)]α[d(x,Ty)]γ[(d(x,Ty)+d(x,Ty))/2]1−α−β−γ, where α , β , γ ∈ ( 0,1 ) with α + β + γ < 1 and some interpolative type contractive conditions. Also, we investigate some geometric properties of Fix(T) under some interpolative type contractions and prove some fixed-disc (resp. fixed-circle) results. Finally, we present a new application to the discontinuous activation functions.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"90 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80293957","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
A counter example on a Borsuk conjecture 一个关于Borsuk猜想的反例
IF 0.8
Applied general topology Pub Date : 2023-04-05 DOI: 10.4995/agt.2023.18176
A. Cholaquidis
{"title":"A counter example on a Borsuk conjecture","authors":"A. Cholaquidis","doi":"10.4995/agt.2023.18176","DOIUrl":"https://doi.org/10.4995/agt.2023.18176","url":null,"abstract":"The  study  of  shape  restrictions  of  subsets  of Rd has  several  applications in many areas, being convexity, r-convexity, and positive reach, some of the most famous, and typically imposed in set estimation.  The following problem was attributed to K. Borsuk, by J. Perkal in 1956:find an r-convex set which is not locally contractible.  Stated in that way is trivial to find such a set.  However, if we ask the set to be equal to  the  closure  of  its  interior  (a  condition  fulfilled  for  instance  if  the set  is  the  support  of  a  probability  distribution  absolutely  continuous with respect to the d-dimensional Lebesgue measure), the problem is much  more  difficult.   We  present  a  counter  example  of  a  not  locally contractible set, which is r-convex.  This also proves that the class of supports with positive reach of absolutely continuous distributions includes strictly the class ofr-convex supports of absolutely continuous distributions.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"27 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74563573","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
Best proximity point for q-ordered proximal contraction in noncommutative Banach spaces 非交换Banach空间中q序近端收缩的最佳邻近点
IF 0.8
Applied general topology Pub Date : 2023-04-05 DOI: 10.4995/agt.2023.18029
A. Bartwal, Shivam Rawat, Ismat Beg
{"title":"Best proximity point for q-ordered proximal contraction in noncommutative Banach spaces","authors":"A. Bartwal, Shivam Rawat, Ismat Beg","doi":"10.4995/agt.2023.18029","DOIUrl":"https://doi.org/10.4995/agt.2023.18029","url":null,"abstract":"We introduce the concept of q-ordered proximal nonunique contraction for the non self mappings and then obtain some proximity point results for these mappings. We also furnish examples to support our claims.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"11 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73064467","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
Hybrid topologies on the real line 实线上的混合拓扑
IF 0.8
Applied general topology Pub Date : 2023-04-05 DOI: 10.4995/agt.2023.18566
T. Richmond
{"title":"Hybrid topologies on the real line","authors":"T. Richmond","doi":"10.4995/agt.2023.18566","DOIUrl":"https://doi.org/10.4995/agt.2023.18566","url":null,"abstract":"Given A ⊆ ℝ , the Hattori space H(A) is the topological space ( ℝ , τA  ) where each a ∈ A has a τA -neighborhood base { ( a − ε , a + ε ) : ε > 0 } and each b ∈ ℝ − A has a τA -neighborhood base { [ b , b + ε ) : ε > 0 } . Thus, τA may be viewed as a hybrid of the Euclidean topology and the lower-limit topology. We investigate properties of Hattori spaces as well as other hybrid topologies on ℝ using various combinations of the discrete, left-ray, lower-limit, upper-limit, and Euclidean topologies. Since each of these topologies is generated by a quasi-metric on ℝ, we investigate hybrid quasi-metrics which generate these hybrid topologies.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"3 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90447323","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
Concrete functors that respect initiality and finality 尊重初始性和终结性的具体函子
IF 0.8
Applied general topology Pub Date : 2023-04-05 DOI: 10.4995/agt.2023.18771
F. Mynard
{"title":"Concrete functors that respect initiality and finality","authors":"F. Mynard","doi":"10.4995/agt.2023.18771","DOIUrl":"https://doi.org/10.4995/agt.2023.18771","url":null,"abstract":"\u0000We study concrete endofunctors of the category of convergence spaces and continuous maps that send initial maps to initial maps or final maps to final maps. The former phenomenon turns out to be fairly common while the latter is rare. In particular, it is shown that the pretopological modification is the coarsest hereditary modifier finer than the topological modifier and this is applied to give a structural interpretation of the role of Fréchet-Urysohn spaces with respect to sequential spaces and of k' -spaces with respect to k -spaces.\u0000","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"60 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78343296","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
Digital semicovering and digital quasicovering maps 数字半覆盖和数字准覆盖地图
IF 0.8
Applied general topology Pub Date : 2023-04-05 DOI: 10.4995/agt.2023.17156
A. Pakdaman
{"title":"Digital semicovering and digital quasicovering maps","authors":"A. Pakdaman","doi":"10.4995/agt.2023.17156","DOIUrl":"https://doi.org/10.4995/agt.2023.17156","url":null,"abstract":"In this paper we introduce notions of digital semicovering and digital quasicovering maps. We show that these are generalizations of digital covering maps and investigate their relations. We will also clarify the relationship between these generalizations and digital path lifting.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82796455","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
Fixed points which belong to the set of unit values of a suitable function on fuzzy metric spaces 模糊度量空间上属于合适函数单位值集合的不动点
IF 0.8
Applied general topology Pub Date : 2023-04-05 DOI: 10.4995/agt.2023.16924
Hayel N. Saleh, M. Imdad, W. Sintunavarat
{"title":"Fixed points which belong to the set of unit values of a suitable function on fuzzy metric spaces","authors":"Hayel N. Saleh, M. Imdad, W. Sintunavarat","doi":"10.4995/agt.2023.16924","DOIUrl":"https://doi.org/10.4995/agt.2023.16924","url":null,"abstract":"In this paper, we introduce the notion of fuzzy (F, φ,β-ψ)-contractive mappings in fuzzy metric spaces and utilize the same to prove some existence and uniqueness fuzzy φ-fixed point results in both M-complete and G-complete fuzzy metric spaces. The obtained results extend, generalize and improve some relevant results of the existing literature. An illustrative example is utilized to demonstrate the usefulness and effectiveness of our results.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"217 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79172705","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
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