Applied General Topology - Vol 08, No 2 (2007)

Tabla de contenidos

Products of straight spaces with compact spaces
Finite products of filters that are compact relative to a class of filters
Relations that preserve compact filters
The Alexandroff Duplicate and its subspaces
The diagonal of a first countable paratopological group, submetrizability, and related results
Completions of pre–uniform spaces
A Survey on Wallman Bases
Sandwich-type characterization of completely regular spaces
On br -closed sets
On countable star-covering properties
CL(R) is simply connected under the Vietoris topology
On the Order Hereditary Closure Preserving Sum Theorem
On complete accumulation points of discrete subsets
Cellularity and density of balleans
cl-Supercontinuous Functions
Lower homomorphisms on additive generalized algebraic lattices
Stone compactification of additive generalized-algebraic lattices

URI permanente para esta colecciónhttps://riunet.upv.es/handle/10251/83052

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Mostrando 1 - 17 de 17

Access status: Abierto ,
Stone compactification of additive generalized-algebraic lattices
(Universitat Politècnica de València, 2007-10-01) Chen, Xueyou; Li, Quingguo; Deng, Zike; National Natural Science Foundation of China
[EN] In this paper, the notions of regular, completely regular, compact additive generalized algebraic lattices are introduced, and Stone compactification is constructed. The following theorem is also obtained. Theorem: An additive generalized algebraic lattice has a Stone compactification if and only if it is regular and completely regular.
Access status: Abierto ,
Lower homomorphisms on additive generalized algebraic lattices
(Universitat Politècnica de València, 2007-10-01) Chen, Xueyou; Deng, Zike; National Natural Science Foundation of China
[EN] In this paper, with the additivity property, the generalized way-below relation and the maximal system of subsets as tools, we prove that all lower homomorphisms between two additive generalized algebraic lattices form an additive generalized algebraic lattice, which yields the classical theorem: the function space between T0-topological spaces is also a T0-topological space with respect to the pointwise convergence topology.
Access status: Abierto ,
cl-Supercontinuous Functions
(Universitat Politècnica de València, 2007-10-01) Singh, D.
[EN] Basic properties of cl-supercontinuity, a strong variant of continuity, due to Reilly and Vamanamurthy [Indian J. Pure Appl. Math., 14 (1983), 767–772], who call such maps clopen continuous, are studied. Sufficient conditions on domain or range for a continuous function to be cl-supercontinuous are observed. Direct and inverse transfer of certain topological properties under cl-supercontinuous functions are studied and existence or nonexistence of certain cl-supercontinuous function with specified domain or range is outlined.
Access status: Abierto ,
Cellularity and density of balleans
(Universitat Politècnica de València, 2007-10-01) Protasov, Igor V.
[EN] A ballean is a set X endowed with some family F of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. Then we define the asymptotic counterparts for dense and open subsets, introduce two cardinal invariants (density and cellularity) of balleans and prove some results concerning relationship between these invariants. We conclude the paper with applications of obtained partitions of left topological group in dense subsets.
Access status: Abierto ,
On complete accumulation points of discrete subsets
(Universitat Politècnica de València, 2007-10-01) Alas, Ofelia T.; Wilson, Richard G.; Consejo Nacional de Ciencia y Tecnología, México
[EN] We introduce a class of spaces in which every discretesubset has a complete accumulation point. Properties of this classare obtained and consistent examples are given to show that this classdiffers from the class of countably compact and the class of compactspaces. A number of questions are posed.
Access status: Abierto ,
On the Order Hereditary Closure Preserving Sum Theorem
(Universitat Politècnica de València, 2007-10-01) Gong, Jianhua; Reilly, Ivan L.
[EN] The main purpose of this paper is to prove the following two theorems, an order hereditary closure preserving sum theorem and an hereditary theorem: (1) If a topological property P satisfies (Σ′) and is closed hereditary, and if V is an order hereditary closure preserving open cover of X and each V ϵ V is elementary and possesses P, then X possesses P. (2) Let a topological property P satisfy (Σ′) and (β), and be closed hereditary. Let X be a topological space which possesses P. If every open subset G of X can be written as an order hereditary closure preserving (in G) collection of elementary sets, then every subset of X possesses P.
Access status: Abierto ,
CL(R) is simply connected under the Vietoris topology
(Universitat Politècnica de València, 2007-10-01) Esty, N.C.
[EN] In this paper we present a proof by construction that the hyperspace CL(R) of closed, nonemtpy subsets of R is simply connected under the Vietoris topology. This is useful in considering the convergence of time scales. We also present a construction of the (known) fact that this hyperspace is also path connected, as part of the proof.
Access status: Abierto ,
On countable star-covering properties
(Universitat Politècnica de València, 2007-10-01) Song, Yan-Kui; National Natural Science Foundation of China
[EN] We introduce two new notions of topological spaces called a countably starcompact space and a countably absolutely countably compact (= countably acc) space. We clarify the relations between these spaces and other related spaces and investigate topological properties of countably starcompact spaces and countably acc spaces. Some examples showing the limitations of our results are also given.
Access status: Abierto ,
On br -closed sets
(Universitat Politècnica de València, 2007-10-01) Ganster, Maximilian; Steiner, Markus
[EN] This paper is closely related to the work of Cao, Greenwood and Reilly in as it expands and completes their fundamental diagram by considering b-closed sets. In addition, we correct a wrong assertion in about βgs-spaces.
Access status: Abierto ,
Sandwich-type characterization of completely regular spaces
(Universitat Politècnica de València, 2007-10-01) Gutiérrez García, Javier; Kubiak, Tomasz; Ministerio de Educación y Ciencia; Universidad del País Vasco/Euskal Herriko Unibertsitatea
[EN] All the higher separation axioms in topology, except for complete regularity, are known to have sandwich-type characterizations. This note provides a characterization of complete regularity in terms of inserting a continuous real-valued function. The known fact that each continuous real valued function on a compact subset o fa Tychonoff space has a continuous extension to the whole space is obtained as a corollary.
Access status: Abierto ,
A Survey on Wallman Bases
(Universitat Politècnica de València, 2007-10-01) García-Máynez, Adalberto
[EN] Wallman bases are frequently used in compactification processes of topological spaces. However, they are also related with quasi–uniform structures and they are useful to characterize some topological properties. We present a brief survey on the subject which supports these statements.
Access status: Abierto ,
Completions of pre–uniform spaces
(Universitat Politècnica de València, 2007-10-01) García-Máynez, Adalberto; Mancio-Toledo, Rubén
[EN] In this paper we prove the existence of a completion of a T0–pre-uniform space (X,U), with the property that each Cauchy filter in (X,U) contains a weakly round filter.
Access status: Abierto ,
The diagonal of a first countable paratopological group, submetrizability, and related results
(Universitat Politècnica de València, 2007-10-01) Arhangelskii, A.V.; Bella, Angelo
[EN] We discuss some properties stronger than Gδ-diagonal. Among other things, we prove that any first countable paratopological group has a Gδ-diagonal of infinite rank and hence also a regular Gδ-diagonal. This answer a question recently asked by Arhangel’skii and Burke.
Access status: Abierto ,
The Alexandroff Duplicate and its subspaces
(Universitat Politècnica de València, 2007-10-01) Caserta, Agata; Watson, Stephen
[EN] We study some topological properties of the class of the Alexandroff duplicates and their subspaces. We give a characterization of metrizability and Lindel¨of properties of subspaces of the Alexandroff duplicate. This characterization clarifies the potential for finding Michael spaces among the subspaces of Alexandroff duplicates.
Access status: Abierto ,
Relations that preserve compact filters
(Universitat Politècnica de València, 2007-10-01) Mynard, Frédéric
[EN] Many classes of maps are characterized as (possibly multi-valued) maps preserving particular types of compact filters.
Access status: Abierto ,
Finite products of filters that are compact relative to a class of filters
(Universitat Politècnica de València, 2007-10-01) Jordan, Francis; Labuda, Iwo; Mynard, Frédéric
[EN] Filters whose product with every countable based countably compact filter is countably compact are characterized.
Access status: Abierto ,
Products of straight spaces with compact spaces
(Universitat Politècnica de València, 2007-10-01) Nishijima, Kusuo; Yamada, Kohzo
[EN] A metric space X is called straight if any continuous real-valued function which is uniformly continuous on each set of a finite cover of X by closed sets, is itself uniformly continuous. Let C be the convergent sequence {1/n : n ϵ N} with its limit 0 in the real line with the usual metric. In this paper, we show that for a straight space X, X × C is straight if and only if X × K is straight for any compact metric space K. Furthermore, we show that for a straight space X, if X × C is straight, then X is precompact. Note that the notion of straightness depends on the metric on X. Indeed, since the real line R with the usual metric is not precompact, R×C is not straight. On the other hand, we show that the product space of an open interval and C is straight.

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