Applied General Topology - Vol 07, No 1 (2006)
https://riunet.upv.es:443/handle/10251/82949
2022-01-24T20:32:30ZOn spaces with the property (wa)
https://riunet.upv.es:443/handle/10251/82970
On spaces with the property (wa)
Song, Yan-Kui
[EN] A space X has the property (wa) (or is a space with the property (wa)) if for every open cover U of X and every dense subspace D of X, there exists a discrete subspace F C D such that St(F, U) = X. In this paper, we give an example of a Tychonoff space without the property (wa), and also study topological properties of spaces with the property (wa) by using the example.
2017-06-16T09:24:48ZOn nearly Hausdorff compactifications
https://riunet.upv.es:443/handle/10251/82969
On nearly Hausdorff compactifications
Shah, Sejal; Das, T.K.
[EN] We introduce and study here the notion of nearly Hausdorffness, a separation axiom, stronger than T1 but weaker than T2. For a space X, from a subfamily of the family of nearly Hausdorff spaces, we construct a compact nearly Hausdorff space rX containing X as a densely C*-embedded subspace. Finally, we discuss when rX is βX.
2017-06-16T09:22:30ZMaking group topologies with, and without, convergent sequences
https://riunet.upv.es:443/handle/10251/82968
Making group topologies with, and without, convergent sequences
Comfort, W.W.; Raczkowski, S.U.; Trigos-Arrieta, F.J.
[EN] (1) Every infinite, Abelian compact (Hausdorff) group K admits 2|K|- many dense, non-Haar-measurable subgroups of cardinality |K|. When K is nonmetrizable, these may be chosen to be pseudocompact. (2) Every infinite Abelian group G admits a family A of 22|G|-many pairwise nonhomeomorphic totally bounded group topologies such that no nontrivial sequence in G converges in any of the topologies T ϵ A. (For some G one may arrange ω(G, T ) < 2|G| for some T ϵ A.) (3) Every infinite Abelian group G admits a family B of 22|G|-many pairwise nonhomeomorphic totally bounded group topologies, with ω (G, T ) = 2|G| for all T ϵ B, such that some fixed faithfully indexed sequence in G converges to 0G in each T ϵ B.
2017-06-16T09:19:32ZTightness of function spaces
https://riunet.upv.es:443/handle/10251/82967
Tightness of function spaces
Lin, Shou
[EN] The purpose of this paper is to give higher cardinality versions of countable fan tightness of function spaces obtained by A. Arhangel’skiı. Let vet(X), ωH(X) and H(X) denote respectively the fan tightness, ω-Hurewicz number and Hurewicz number of a space X, then vet(Cp(X)) = ωH(X) = sup{H(Xn) : n 2 N}.
2017-06-16T09:16:13ZOn RG-spaces and the regularity degree
https://riunet.upv.es:443/handle/10251/82956
On RG-spaces and the regularity degree
Raphael, R.; Woods, R.G.
[EN] We continue the study of a lattice-ordered ring G(X), associated with the ring C(X). Following, X is called RG when G(X) = C(Xδ). An RG-space must have a dense set of very weak P-points. It must have a dense set of almost-P-points if Xδ is Lindelöf, or if the continuum hypothesis holds and C(X) has small cardinality. Spaces which are RG must have finite Krull dimension when taken with respect to the prime z-ideals of C(X). There is a notion of regularity degree defined via the functions in G(X). Pseudocompact spaces and metric spaces of finite regularity degree are characterized.
2017-06-16T09:12:36ZTopological groups: local versus global
https://riunet.upv.es:443/handle/10251/82955
Topological groups: local versus global
Arhangelskii, A.V.; Uspenskij, Vladimir V.
[EN] It is well known that locally compact groups are paracompact. We observe that this theorem can be generalized as follows: every locally paracompact group is paracompact. We prove a more general version of this statement using quotients. Similar ‘local implies global’ theorems hold also for many other properties, such as normality, metacompactness, stratifiability, etc.
2017-06-16T09:10:12ZOn i-topological spaces: generalization of the concept of a topological space via ideals
https://riunet.upv.es:443/handle/10251/82954
On i-topological spaces: generalization of the concept of a topological space via ideals
Zvina, Irina
[EN] The aim of this paper is to generalize the structure of a topological space, preserving its certain topological properties. The main idea is to consider the union and intersection of sets modulo “small” sets which are defined via ideals. Developing the concept of an i-topological space and studying structures with compatible ideals, we are concerned to clarify the necessary and sufficient conditions for a new space to be homeomorphic, in some certain sense, to a topological space.
2017-06-16T09:06:23ZCriteria of strong nearest-cross points and strong best approximation pairs
https://riunet.upv.es:443/handle/10251/82953
Criteria of strong nearest-cross points and strong best approximation pairs
Pan, Wenxi; Xu, Jingshi
[EN] The concept of strong nearest-cross point (strong n.c. point) is introduced, which is the generalization of strong uniqueness of best approximation from a single point. The relation connecting to localization is discussed. Some criteria of strong n.c. points are given. The strong best approximation pairs are also studied.
2017-06-16T09:04:31ZWeakly metrizable pseudocompact groups
https://riunet.upv.es:443/handle/10251/82952
Weakly metrizable pseudocompact groups
Dikranjan, Dikran; Giordano Bruno, Anna; Milan, Chiara
[EN] We study various weaker versions of metrizability for pseudocompact abelian groups G: singularity (G possesses a compact metrizable subgroup of the form mG, m > 0), almost connectedness (G is metrizable modulo the connected component) and various versions of extremality in the sense of Comfort and co-authors (s-extremal, if G has no proper dense pseudocompact subgroups, r-extremal, if G admits no proper pseudocompact refinement). We introduce also weaklyextremal pseudocompact groups (weakening simultaneously s-extremal and r-extremal). It turns out that this “symmetric” version of ex-tremality has nice properties that restore the symmetry, to a certain extent, in the theory of extremal pseudocompact groups obtaining simpler uniform proofs of most of the known results. We characterize doubly extremal pseudocompact groups within the class of s-extremal pseudocompact groups. We give also a criterion for r-extremality for connected pseudocompact groups.
2017-06-16T09:02:03Z