Star-Hurewicz Modulo an Ideal Property In Topological Spaces

2021 ◽  
Vol 88 (1-2) ◽  
pp. 33
Author(s):  
Manoj Bhardwaj ◽  
B. K. Tyagi ◽  
Sumit Singh
Keyword(s):  
Topological Spaces ◽  
Extremally Disconnected ◽  
Ideal Property

In this paper, a class of star-Hurewicz modulo an ideal spaces is introduced and studied. For an ideal <em>K</em> of finite subsets of N, a characterization of weakly star-<em>K</em>-Hurewicz extremally disconnected spaces is given using ideal. It is shown that star-Hurewicz modulo an ideal property is hereditary under clopen subspaces. In this manner we obtained relationships of star-Hurewicz modulo an ideal property with other existing Hurewicz properties in literature.

scholarly journals £-Single Valued Extremally Disconnected Ideal Neutrosophic Topological Spaces

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 53
Author(s):  
Fahad Alsharari
Keyword(s):  
Topological Spaces ◽  
Neutrosophic Sets ◽  
Extremally Disconnected ◽  
Fundamental Properties ◽  
Separation Axioms ◽  
New Concepts ◽  
Definition Of

This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic £-closed and £-open sets. The definition of £-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, the concepts of £-single valued neutrosophic extremally disconnected and £-single valued neutrosophic normal spaces are established. As a result, a useful implication diagram between the r-single valued neutrosophic ideal open sets is obtained. Finally, some kinds of separation axioms, namely r-single valued neutrosophic ideal-Ri (r-SVNIRi, for short), where i={0,1,2,3}, and r-single valued neutrosophic ideal-Tj (r-SVNITj, for short), where j={1,2,212,3,4}, are introduced. Some of their characterizations, fundamental properties, and the relations between these notions have been studied.

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.

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 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.

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