Applied General Topology - Vol 12, No 1 (2011)https://riunet.upv.es:443/handle/10251/869582022-01-28T23:21:20Z2022-01-28T23:21:20ZSome remarks on stronger versions of the Boundary Problem for Banach spacesHardtke, Jan-Davidhttps://riunet.upv.es:443/handle/10251/869812020-10-06T15:33:42Z2017-09-11T12:23:58ZSome remarks on stronger versions of the Boundary Problem for Banach spaces
Hardtke, Jan-David
[EN] Let X be a real Banach space. A subset B of the dual unit sphere of X is said to be a boundary for X, if every element of X attains its norm on some functional in B. The well-known Boundary Problem originally posed by Godefroy asks whether a bounded subset of X which is compact in the topology of pointwise convergence on B is already weakly compact. This problem was recently solved by Pfitzner in the positive. In this note we collect some stronger versions of the solution to the Boundary Problem, most of which are restricted to special types of Banach spaces. We shall use the results and techniques of Pfitzner, Cascales et al., Moors and others.
2017-09-11T12:23:58ZIntroduction to generalized topological spacesZvina, Irinahttps://riunet.upv.es:443/handle/10251/869792020-10-06T15:33:42Z2017-09-11T12:20:50ZIntroduction to generalized topological spaces
Zvina, Irina
[EN] We introduce the notion of generalized topological space (gt-space). Generalized topology of gt-space has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. The family of small subsets of a gt-space forms an ideal that is compatible with the generalized topology. To support the definition of gt-space we prove the frame embedding modulo compatible ideal theorem. Weprovide some examples of gt-spaces and study key topological notions (continuity, separation axioms, cardinal invariants) in terms of generalized spaces.
2017-09-11T12:20:50ZA Kuratowski-Mrówka type characterization of fibrewise compactnessNeira U.Clara M.https://riunet.upv.es:443/handle/10251/869762021-11-08T07:57:09Z2017-09-11T12:17:14ZA Kuratowski-Mrówka type characterization of fibrewise compactness
Neira U.; Clara M.
[EN] In this paper a Kuratowski-Mrówka type characterization of fibrewisecompact topological spaces is presented.
2017-09-11T12:17:14ZHypercyclic abelian semigroup of matrices on Cn and Rn and k-transitivity (k ≥ 2)Ayadi, Adlenehttps://riunet.upv.es:443/handle/10251/869742020-10-06T15:33:42Z2017-09-11T12:15:07ZHypercyclic abelian semigroup of matrices on Cn and Rn and k-transitivity (k ≥ 2)
Ayadi, Adlene
[EN] We prove that the minimal number of matrices on Cn required to forma hypercyclic abelian semigroup on Cn is n+1. We also prove that theaction of any abelian semigroup finitely generated by matrices on Cnor Rn is never k-transitive for k 2. These answer questions raised byFeldman and Javaheri.
2017-09-11T12:15:07ZCharacterizing meager paratopological groupsBanak, TarasGuran, IgorRavsky, Alexhttps://riunet.upv.es:443/handle/10251/869732021-11-08T07:57:09Z2017-09-11T12:11:34ZCharacterizing meager paratopological groups
Banak, Taras; Guran, Igor; Ravsky, Alex
[EN] We prove that a Hausdorff paratopological group G is meager if andonly if there are a nowhere dense subset A G and a countable setC G such that CA = G = AC.
2017-09-11T12:11:34Zp-Compact, p-Bounded and p-CompleteVera Mendoza, Rigobertohttps://riunet.upv.es:443/handle/10251/869702021-11-08T07:57:09Z2017-09-11T12:08:43Zp-Compact, p-Bounded and p-Complete
Vera Mendoza, Rigoberto
[EN] In this paper the nonstandard theory of uniform topological spaces isapplied with two main objectives: (1) to give a nonstandard treatmentof Bernstein’s concept of p-compactness with additional results, (2) tointroduce three new concepts (p,q)-compactness, p-totally boundednessand p-completeness. I prove some facts about them and how these threeconcepts are related with p-compactness.
2017-09-11T12:08:43ZThe equality of the Patch topology and the Ultrafilter topology: A shortcutRuza, Luz M.Vielma, Jorgehttps://riunet.upv.es:443/handle/10251/869682021-11-08T07:57:09Z2017-09-11T12:04:31ZThe equality of the Patch topology and the Ultrafilter topology: A shortcut
Ruza, Luz M.; Vielma, Jorge
[EN] In this work R denotes a commutative ring with non-zero identity andwe prove that the patch topology and the ultrafilter topology definedon the prime spectrum of R are equal, in a different way as the givenby Marco Fontana and K. Alan Loper
2017-09-11T12:04:31ZThe structure of the poset of regular topologies on a setAlas, Ofelia T.Wilson, Richard G.https://riunet.upv.es:443/handle/10251/869612021-11-08T07:57:10Z2017-09-11T11:56:55ZThe structure of the poset of regular topologies on a set
Alas, Ofelia T.; Wilson, Richard G.
[EN] We study the subposet E3(X) of the lattice L1(X) of all T1-topologies on a set X, being the collections of all T3 topologies on X, with a view to deciding which elements of this partially ordered set have and which do not have immediate predecessors. We show that each regular topology which is not R-closed does have such a predecessor and as a corollary we obtain a result of Costantini that each non-compact Tychonoff space has an immediate predecessor in E3. We also consider the problem of when an R-closed topology is maximal R-closed.
2017-09-11T11:56:55Z