{"title":"Diagonals of separately continuous maps with values in box products","authors":"O. Karlova, V. Mykhaylyuk","doi":"10.1515/taa-2018-0002","DOIUrl":"https://doi.org/10.1515/taa-2018-0002","url":null,"abstract":"Abstract We prove that if X is a paracompact connected space and Z = ∏s∈S Zs is a product of a family of equiconnected metrizable spaces endowed with the box topology, then for every Baire-one map g : X → Z there exists a separately continuous map f : X2 → Z such that f (x, x) = g(x) for all x ∈ X.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"6 1","pages":"26 - 33"},"PeriodicalIF":0.0,"publicationDate":"2017-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2018-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43681277","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}
{"title":"Balanced and functionally balanced P-groups","authors":"Menachem Shlossberg","doi":"10.1515/taa-2018-0006","DOIUrl":"https://doi.org/10.1515/taa-2018-0006","url":null,"abstract":"Abstract In relation to Itzkowitz’s problem [5], we show that a c-bounded P-group is balanced if and only if it is functionally balanced.We prove that for an arbitrary P-group, being functionally balanced is equivalent to being strongly functionally balanced. A special focus is given to the uniform free topological group defined over a uniform P-space. In particular, we show that this group is (functionally) balanced precisely when its subsets Bn, consisting of words of length at most n, are all (resp., functionally) balanced.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"6 1","pages":"53 - 59"},"PeriodicalIF":0.0,"publicationDate":"2017-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2018-0006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47575804","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}
{"title":"A model of quotient spaces","authors":"H. Hattab","doi":"10.1515/taa-2017-0003","DOIUrl":"https://doi.org/10.1515/taa-2017-0003","url":null,"abstract":"Abstract Let R be an open equivalence relation on a topological space E. We define on E a new equivalence relation ̃ℜ̅ by x̃ ̃ℜ̅y if the closure of the R-trajectory of x is equal to the closure of the R-trajectory of y. The quotient space E/̃ ̃ℜ̅ is called the trajectory class space. In this paper, we show that the space E/̃ ̃ℜ̅ is a simple model of the quotient space E/R. This model can provide a finite model. Some applications to orbit spaces of groups of homeomorphisms and leaf spaces are given.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"5 1","pages":"13 - 18"},"PeriodicalIF":0.0,"publicationDate":"2017-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2017-0003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47909374","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}
{"title":"Residuation in orthomodular lattices","authors":"I. Chajda, H. Länger","doi":"10.1515/taa-2017-0001","DOIUrl":"https://doi.org/10.1515/taa-2017-0001","url":null,"abstract":"Abstract We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lattice. In this case, also the converse statement is true and the corresponence is nearly one-to-one.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"5 1","pages":"1 - 5"},"PeriodicalIF":0.0,"publicationDate":"2017-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2017-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44658273","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}
{"title":"Versatile asymmetrical tight extensions","authors":"O. O. Otafudu, Zechariah Mushaandja","doi":"10.1515/taa-2017-0002","DOIUrl":"https://doi.org/10.1515/taa-2017-0002","url":null,"abstract":"Abstract We show that the image of a q-hyperconvex quasi-metric space under a retraction is q-hyperconvex. Furthermore, we establish that quasi-tightness and quasi-essentiality of an extension of a T0-quasi-metric space are equivalent.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"5 1","pages":"12 - 6"},"PeriodicalIF":0.0,"publicationDate":"2017-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2017-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45336209","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}
{"title":"On locally compact semitopological O-bisimple inverse ω-semigroups","authors":"O. Gutik","doi":"10.1515/taa-2018-0008","DOIUrl":"https://doi.org/10.1515/taa-2018-0008","url":null,"abstract":"Abstract We describe the structure of Hausdorff locally compact semitopological O-bisimple inverse ω- semigroups with compact maximal subgroups. In particular, we show that a Hausdorff locally compact semitopological O-bisimple inverse ω-semigroup with a compact maximal subgroup is either compact or it is a topological sum of its H-classes. We describe the structure of Hausdorff locally compact semitopological O-bisimple inverse ω-semigroups with a monothetic maximal subgroups. We show the following dichotomy: a T1 locally compact semitopological Reilly semigroup (B(Z+, θ)0, τ) over the additive group of integers Z+, with adjoined zero and with a non-annihilating homomorphism is either compact or discrete. At the end we establish some properties of the remainder of the closure of the discrete Reilly semigroup B(Z+, θ) in a semitopological semigroup.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"6 1","pages":"101 - 77"},"PeriodicalIF":0.0,"publicationDate":"2017-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2018-0008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45530183","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}
{"title":"Hermite-Hadamard Type Inequalities for convex functions via generalized fractional integral operators","authors":"E. Set, Abdurrahman Gözpınar","doi":"10.1515/taa-2017-0009","DOIUrl":"https://doi.org/10.1515/taa-2017-0009","url":null,"abstract":"Abstract In this present work, the authors establish a new integral identity involving generalized fractional integral operators and by using this fractional-type integral identity, obtain some new Hermite-Hadamard type inequalities for functions whose first derivatives in absolute value are convex. Relevant connections of the results presented here with those earlier ones are also pointed out.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"5 1","pages":"55 - 62"},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2017-0009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67317874","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}
{"title":"Topological Rough Groups","authors":"Nurettin Bagirmaz, I. Içen, A. Özcan","doi":"10.1515/taa-2016-0004","DOIUrl":"https://doi.org/10.1515/taa-2016-0004","url":null,"abstract":"Abstract The concept of topological group is a simple combination of the concepts of abstract group and topological space. The purpose of this paper is to combine the concepts of topological space and rough groups; called topological rough groups on an approximation space.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2016-0004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67317809","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}
{"title":"On unitary extensions and unitary completions of topological monoids","authors":"B. Averbukh","doi":"10.1515/taa-2016-0003","DOIUrl":"https://doi.org/10.1515/taa-2016-0003","url":null,"abstract":"Abstract The concept of a unitary Cauchy net in an arbitrary Hausdorff topological monoid generalizes the concept of a fundamental sequence of reals. We construct extensions of this monoid where all its unitary Cauchy nets converge.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2016-0003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67317652","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}
{"title":"Quotients of Strongly Realcompact Groups","authors":"L. Morales, M. Tkachenko","doi":"10.1515/taa-2016-0002","DOIUrl":"https://doi.org/10.1515/taa-2016-0002","url":null,"abstract":"Abstract A topological group is strongly realcompact if it is topologically isomorphic to a closed subgroup of a product of separable metrizable groups. We show that if H is an invariant Čech-complete subgroup of an ω-narrow topological group G, then G is strongly realcompact if and only if G/H is strongly realcompact. Our proof of this result is based on a thorough study of the interaction between the P-modification of topological groups and the operation of taking quotient groups.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2016-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67317543","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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