Applied General Topology - Vol 13, No 1 (2012)
https://riunet.upv.es:443/handle/10251/87171
2019-11-12T21:24:21ZRelative dimension r-dim and finite spaces
https://riunet.upv.es:443/handle/10251/87191
Relative dimension r-dim and finite spaces
Megaritis, A.C.
[EN] In a relative covering dimension is defined and studied which is denoted by r-dim. In this paper we give an algorithm of polynomial order for computing the dimension r-dim of a pair (Q,X), where Q is a subset of a finite space X, using matrix algebra.
2017-09-13T09:30:26ZTopological conditions for the representation of preorders by continuous utilities
https://riunet.upv.es:443/handle/10251/87190
Topological conditions for the representation of preorders by continuous utilities
Minguzzi, E.
[EN] We remove the Hausdorff condition from Levin's theorem on the representation of preorders by families of continuous utilities. We compare some alternative topological assumptions in a Levin's type theorem, and show that they are equivalent to a Polish space assumption.
2017-09-13T09:27:31ZRandom selection of Borel sets II
https://riunet.upv.es:443/handle/10251/87186
Random selection of Borel sets II
Günther, Bernd
[EN] The theory of random Borel sets as presented in part I of this paper is developed further. Special attention is payed to the reconstruction of the topology of the underlying space from our presentation of the measure algebra, to an analysis of capacities in context of random Borel sets, to inspection processes on the unit segment and to the Markov process of random allocation.
2017-09-13T09:20:03ZHereditary separability in Hausdorff continua
https://riunet.upv.es:443/handle/10251/87185
Hereditary separability in Hausdorff continua
Daniel, D.; Tuncali, M.
[EN] We consider those Hausdorff continua S such that each separable subspace of S is hereditarily separable. Due to results of Ostaszewski and Rudin, respectively, all monotonically normal spaces and therefore all continuous Hausdorff images of ordered compacta also have this property. Our study focuses on the structure of such spaces that also possess one of various rim properties, with emphasis given to rim-separability. In so doing we obtain analogues of results of M. Tuncali and I. Loncar, respectively.
2017-09-13T09:18:14ZAspects of RG-spaces
https://riunet.upv.es:443/handle/10251/87184
Aspects of RG-spaces
Abohalfya, F.; Raphael, R.
[EN] A Tychonoff space X which satisfies the property that G(X) = C(Xδ) is called an RG-space, where G(X) is the minimal regular ring extension of C(X) inside F(X), the ring of all functions from X to R, and Xδ is the topology on X generated by its Gδ-sets. We correct an error tha twe found in the proof of and show that RG-spaces must satisfy a finite dimensional condition.
We also introduce a new class of topological spaces which we call almost k-Baire spaces. The class of almost Baire spaces is a particular instance. We show that every RG-space is an almost Baire space but not necessarily a Baire space. However RG-spaces of countable pseudocharacter must be Baire and, furthermore, their dense sets have dense interiors.
2017-09-13T09:16:07ZOn density and π-weight of Lp(βN,R, μ)
https://riunet.upv.es:443/handle/10251/87181
On density and π-weight of Lp(βN,R, μ)
Iurato, Giuseppe
[EN] The new topological concept of selective separability is able to give some estimates for density and π-weight of the Lebesgue space Lp(βN,R, μ) with 1 ≤ p < +∞. In particular, we deduce a purely topological proof of the non-separability of such a space.
2017-09-13T09:13:50ZHausdorff closed extensions of pre-uniform spaces
https://riunet.upv.es:443/handle/10251/87179
Hausdorff closed extensions of pre-uniform spaces
García-Máynez, Adalberto; Mancio-Toledo, Rubén
[EN] The family of densely finite open covers of a Hausdorff space X determines a completable pre-uniformity on X and the canonical completion X is Hausdorff closed. We compare X with the Katetov extension kX of X and give sufficient conditions for the non-equivalence of kX and X.
2017-09-13T09:11:24ZExtending maps between pre-uniform spaces
https://riunet.upv.es:443/handle/10251/87177
Extending maps between pre-uniform spaces
García-Máynez, Adalberto; Mancio-Toledo, Rubén
[EN] We give sufficient conditions on a uniformly continuous map f: (X,U) → (Y, V ) between completable T1-pre-uniform spaces (X,U), (Y, V ) to have a continuous or a uniformly continuous extension f:X → Y between the corresponding completions.
2017-09-13T09:07:08ZSome results and examples concerning Whyburn spaces
https://riunet.upv.es:443/handle/10251/87175
Some results and examples concerning Whyburn spaces
Alas, Ofelia T.; Madriz-Mendoza, Maira; Wilson, Richard G.
[EN] We prove some cardinal inequalities valid in the classes of Whyburn and hereditarily weakly Whyburn spaces and we construct examples of non-Whyburn and non-weakly Whyburn spaces to illustrate that some previously known results cannot be generalized.
2017-09-13T09:03:56ZOn cofree S-spaces and cofree S-flows
https://riunet.upv.es:443/handle/10251/87174
On cofree S-spaces and cofree S-flows
Khosravi, Behnam
[EN] Let S-Tych be the category of Tychonoff S-spaces for a topological monoid S. We study the cofree S-spaces and cofree S-flows over topological spaces and we prove that for any topological space X and a topological monoid S, the function space C(S,X) with the compact-open topology and the action s · f = (t → f(st)) is the cofree S-space over X if and only if the compact-open topology is admissible and Tychonoff. Finally we study injective S-spaces and we characterize injective cofree S-spaces, when the compact-open topology is admissible and Tychonoff. As a consequence of this result, we characterize the cofree S-spaces and cofree S-flows, when S is a locally compact topological monoid.
2017-09-13T09:00:13Z