A characterization of a class of categories of topological spaces

1978 ◽  
Vol 30 (1) ◽  
pp. 304-316 ◽  
Author(s):  
Rudolf-E. Hoffmann
Keyword(s):  
Topological Spaces

scholarly journals Homological epimorphisms, homotopy epimorphisms and acyclic maps

2020 ◽  
Vol 32 (6) ◽  
pp. 1395-1406
Author(s):  
Joseph Chuang ◽  
Andrey Lazarev
Keyword(s):  
Wide Class ◽  
Topological Spaces ◽  
Loop Spaces ◽  
Graded Algebras ◽  
Differential Graded Algebras ◽  
Algebraic Description ◽  
Acyclic Map ◽  
Induced Maps

AbstractWe show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description for these induced maps in terms of derived localization.

scholarly journals Orderability of topological spaces by continuous preferences

2001 ◽  
Vol 27 (8) ◽  
pp. 505-512 ◽  
Author(s):  
José Carlos Rodríguez Alcantud
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Properties ◽  
Linear Orders ◽  
Mathematical Economics

We extend van Dalen and Wattel's (1973) characterization of orderable spaces and their subspaces by obtaining analogous results for two larger classes of topological spaces. This type of spaces are defined by considering preferences instead of linear orders in the former definitions, and possess topological properties similar to those of (totally) orderable spaces (cf. Alcantud, 1999). Our study provides particular consequences of relevance in mathematical economics; in particular, a condition equivalent to the existence of a continuous preference on a topological space is obtained.

Characterization of Certain Classes of Spaces With Gδ Points as Open Images of Metric Spaces

1975 ◽  
Vol 27 (6) ◽  
pp. 1229-1238
Author(s):  
Kenneth C. Abernethy
Keyword(s):  
Metric Spaces ◽  
Topological Spaces ◽  
Generalized Metric Spaces ◽  
The Past ◽  
Generalized Metric

The study of metrization has led to the development of a number of new topological spaces, called generalized metric spaces, within the past fifteen years. For a survey of results in metrization theory involving many of these spaces, the reader is referred to [13]. Quite a few of these generalized metric spaces have been studied extensively, somewhat independently of their role in metrization theorems. Specifically, we refer here to characterizations of these spaces by various workers as images of metric spaces. Results in this area have been obtained by Alexander [2], Arhangel'skii [3], Burke [5], Heath [10], Michael [15], Nagata [16], and the author [1], to mention a few. Later we will recall specifically some of these results.

A Note on Extending Locally Finite Collections

1976 ◽  
Vol 19 (1) ◽  
pp. 117-119
Author(s):  
H. L. Shapiro ◽  
F. A. Smith
Keyword(s):  
Topological Space ◽  
Set Cover ◽  
Topological Spaces ◽  
Locally Finite ◽  
Whole Space

Recently there has been a great deal of interest in extending refinements of locally finite and point finite collections on subsets of certain topological spaces. In particular the first named author showed that a subset S of a topological space X is P-embedded in X if and only if every locally finite cozero-set cover on S has a refinement that can be extended to a locally finite cozero-set cover of X. Since then many authors have studied similar types of embeddings (see [1], [2], [3], [4], [6], [8], [9], [10], [11], and [12]). Since the above characterization of P-embedding is equivalent to extending continuous pseudometrics from the subspace S up to the whole space X, it is natural to wonder when can a locally finite or a point finite open or cozero-set cover on S be extended to a locally finite or point-finite open or cozero-set cover on X.

scholarly journals Ordinary Single Valued Neutrosophic Topological Spaces

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1075 ◽  
Author(s):  
Kim ◽  
Smarandache ◽  
Lee ◽  
Hur
Keyword(s):  
Topological Spaces ◽  
Neighborhood System

We define an ordinary single valued neutrosophic topology and obtain some of its basicproperties. In addition, we introduce the concept of an ordinary single valued neutrosophic subspace.Next, we define the ordinary single valued neutrosophic neighborhood system and we show thatan ordinary single valued neutrosophic neighborhood system has the same properties in a classicalneighborhood system. Finally, we introduce the concepts of an ordinary single valued neutrosophicbase and an ordinary single valued neutrosophic subbase, and obtain two characterizations of anordinary single valued neutrosophic base and one characterization of an ordinary single valuedneutrosophic subbase.

Four-Dimension Equivalences

1968 ◽  
Vol 20 ◽  
pp. 48-50 ◽  
Author(s):  
J. R. Gard ◽  
R. D. Johnson
Keyword(s):  
Topological Spaces ◽  
Covering Dimension ◽  
Closed Set ◽  
Set Separation

The object of this paper is to establish the equivalence of four functionrelated dimension concepts in arbitrary topological spaces. These concepts involve stability of functions (3, p. 74), the modification of covering dimension involving basic covers (1, p. 243) (which is equivalent to Yu. M. Smirnov's definition using normal covers), the definition involving essential mappings (2, p. 496), and a modification of the closed set separation characterization of dimension in (3, p. 35).

Natural extension of EF-spaces and EZ-spaces to the pointfree context

2019 ◽  
Vol 69 (5) ◽  
pp. 979-988
Author(s):  
Jissy Nsonde Nsayi
Keyword(s):  
Closed Subset ◽  
Natural Extension ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Tychonoff Space ◽  
Regular Closed

Abstract Two problems concerning EF-frames and EZ-frames are investigated. In [Some new classes of topological spaces and annihilator ideals, Topology Appl. 165 (2014), 84–97], Tahirefar defines a Tychonoff space X to be an EF (resp., EZ)-space if disjoint unions of clopen sets are completely separated (resp., every regular closed subset is the closure of a union of clopen subsets). By extending these notions to locales, we give several characterizations of EF and EZ-frames, mostly in terms of certain ring-theoretic properties of 𝓡 L, the ring of real-valued continuous functions on L. We end by defining a qsz-frame which is a pointfree context of qsz-space and, give a characterization of these frames in terms of rings of real-valued continuous functions on L.

On special operations on Ω-closeness on topological spaces

2015 ◽  
Vol 08 (03) ◽  
pp. 1550059
Author(s):  
S. A. Abd-El Baki ◽  
O. R. Sayed
Keyword(s):  
Topological Spaces ◽  
Special Operations ◽  
Closed Sets ◽  
Continuous Maps

In this paper, the concepts of [Formula: see text]-closed and [Formula: see text]-continuous maps are introduced and several properties of them are investigated. These concepts are used to obtain several results concerning the preservation of [Formula: see text]-closed sets. Moreover, we use [Formula: see text]-closed and [Formula: see text]-continuous maps to obtain a characterization of semi-[Formula: see text] spaces.

scholarly journals A characterization of normed M-spaces

1983 ◽  
Vol 24 (1) ◽  
pp. 89-92 ◽  
Author(s):  
Garfield C. Schmidt
Keyword(s):  
Linear Space ◽  
Linear Structure ◽  
Topological Spaces ◽  
Intrinsic Properties ◽  
Small Step ◽  
Linear Lattice ◽  
Linear Spaces ◽  
And Topology ◽  
Necessary And Sufficient

Linear spaces on which both an order and a topology are defined and related in various ways have been studied for some time now. Given an order on a linear space it is sometimes possible to define a useful topology using the order and linear structure. In this note we focus on a special type of space called a linear lattice and determine those lattice properties which are both necessary and sufficient for the existence of a classical norm, called an M-norm, for the lattice. This result is a small step in a program to determine which intrinsic order properties of an ordered linear space are necessary and sufficient for the existence of various given types of topologies for the space. This study parallels, in a certain sense, the study of purely topological spaces to determine intrinsic properties of a topology which make it metrizable and the study of the relation between order and topology on spaces which have no algebraic structure, or. algebraic structures other than a linear one.

A characterization of commutative rings whose maximal ideal spectrum is Noetherian

2018 ◽  
Vol 17 (01) ◽  
pp. 1850003 ◽  
Author(s):  
Sina Hedayat ◽  
Esmaeil Rostami
Keyword(s):  
Maximal Ideal ◽  
Commutative Rings ◽  
Proper Ideal ◽  
Topological Spaces ◽  
Finite Intersection ◽  
Ideal Formula ◽  
Maximal Spectrum

An ideal [Formula: see text] of a ring [Formula: see text] is called pseudo-irreducible if [Formula: see text] cannot be written as an intersection of two comaximal proper ideals of [Formula: see text]. In this paper, it is shown that the maximal spectrum of [Formula: see text] is Noetherian if and only if every proper ideal of [Formula: see text] can be expressed as a finite intersection of pseudo-irreducible ideals. Using a result of Hochster, we characterize all [Formula: see text] quasi-compact Noetherian topological spaces.

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