Journal•ISSN: 0016-660X
General Topology and Its Applications
Elsevier BV
About: General Topology and Its Applications is an academic journal. The journal publishes majorly in the area(s): Hausdorff space & Space (mathematics). Over the lifetime, 274 publications have been published receiving 4515 citations.
Topics: Hausdorff space, Space (mathematics), Topological space, Locally compact space, Metrization theorem
Papers
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TL;DR: In this paper, the images under five kinds of quotient maps of several standard types of topological spaces were studied. But the authors focused on the images with respect to the topological topology.
Abstract: This paper studies the images, under five kinds of quotient maps, of several standard types of topological spaces.
213 citations
TL;DR: In this article, the authors show that the following properties are not preserved by passage to the free abelian group: normal, k- sequential, Frechet, Lindelof, paracompact, countably compact, sequentially compact, etc.
Abstract: Main Theorem. The free abelian topological group over a Tychonoff1 space contains as a closed subspace a homeomorphic copy of each finite power of the space. A major and immediate corollary of this theorem is: If P is a closed hereditary property of Tychonoff spaces, and if the free abelian topological group over a Tychonoff spaces has P , then so does every finite power of the space. In particular, the corollary shows that the following properties are not preserved by passage to the free abelian group: normal, k- sequential, Frechet, Lindelof, paracompact, pseudocompact, countably compact, sequentially compact, etc.
211 citations
TL;DR: In this article, a characterization of minimal prime filters in the lattice IX containing a given filter in IX by means of ultra-filters on X is presented, which enables us to characterize fuzzy compactness and fuzzy continuity.
Abstract: In the first paragraph we study filters in the lattice IX, where I is the unitinterval and X an arbitrary set. The main result of this section is a characterization of minimal prime filters in IX containing a given filter in IX by means of ultrafilters on X. In the second paragraph we apply the results of the previous section to define convergence in a fuzzy topological space which enables us to characterize fuzzy compactness and fuzzy continuity.
197 citations
TL;DR: In this article, the authors propose the concept of nearness, which unifies various concepts of topological structures, such as topological Ro-spaces, continuous maps, uniform spaces, and contiguity spaces.
Abstract: This paper offers solutions for two problems which have attracted many topologists over the years: 1. (1) It provides a natural and reasonably simple concept of “nearness” which unifies various concepts of “topological structures” in the sense that the category Near of all nearness spaces and nearness preserving maps contains the categories (a) of all topological Ro-spaces and continuous maps, (b) of all uniform spaces and uniformly continuous maps (Weil [34], Turkey [33]), (c) of all proximity spaces and δ-maps (Efremovic [9], Smirnov [28,29]), (d) of all contiguity spaces and contiguity maps (Ivanova and Ivanov [17]) as nicely embedded (either bireflective or bicoreflective) full (!) subcategories. 2. (2) It provides a general method by means of which as many T1-extension of a T1-space can be obtained as might be reasonably expected; namely, all strict extensions (in the sense of Banaschewski [3]).
167 citations
TL;DR: In this article, countably bi-quotient mappings are studied and used to characterize sequential, Frechet, strong accessibility, strongly Frechet and strongly k-spaces, each generalization of first countability.
Abstract: Sequence-covering and countably bi-quotient mappings are studied and used to characterize sequential, Frechet, strong accessibility, strongly Frechet, and strongly k ′-spaces. A sequence-covering mapping has a definition analogous to that of a compact-covering mapping, while a countably bi-quotient mapping is a weakening of a bi-quotient mapping. Strong accessibility, strongly Frechet, and strongly k ′-spaces, each generalizations of first countability, are also studied.
130 citations