scholarly journals Weakly m-compact via a hereditary class

2021 ◽  
Vol 39 (3) ◽  
pp. 123-135
Author(s):  
Abdo Qahis ◽  
Heyam Hussain AlJarrah ◽  
Takashi Noiri
Keyword(s):  
Topological Spaces ◽  
Compact Spaces ◽  
Hereditary Class ◽  
Compact Subsets

The aim of this paper is to introduce and study some types of m-compactness with respect to a hereditary class called weakly mH-compact spaces and weakly mH-compact subsets. We will provide several characterizations of weakly mH-compact spaces and investigate their relationships with some other classes of generalized topological spaces.

scholarly journals $\mu$-compactness with respect to a hereditary class

2015 ◽  
Vol 34 (2) ◽  
pp. 231-236 ◽  
Author(s):  
C. Carpintero ◽  
E. Rosas ◽  
Margot Salas-Brown ◽  
J. Sanabria
Keyword(s):  
Topological Spaces ◽  
Compact Spaces ◽  
Hereditary Class

We define and study the notion of compactness in generalized topological spaces with respect to a hereditary class: $\mu\mathcal{H}$-compact spaces.

scholarly journals Applications on operations on weakly compact generalized topological spaces

2020 ◽  
Vol 12 (2) ◽  
pp. 461-467
Author(s):  
B. Roy ◽  
T. Noiri
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Weakly Compact ◽  
Compact Spaces ◽  
Generalized Topological Space ◽  
Compact Subsets

In this paper, we have introduced the notion of operations on a generalized topological space $(X,\mu)$ to investigate the notion of $\gamma_{_\mu}$-compact subsets of a generalized topological space and to study some of its properties. It is also shown that, under some conditions, $\gamma_{_\mu}$-compactness of a space is equivalent to some other weak forms of compactness. Characterizations of such sets are given. We have then introduced the concept of $\gamma_{_\mu}$-$T_{_2}$ spaces to study some properties of $\gamma_{_\mu}$-compact spaces. This operation enables us to unify different results due to S. Kasahara.

scholarly journals On $$\psi _{{\mathcal{H}}}( . )$$-operator in weak structure spaces with hereditary classes

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
H. M. Abu-Donia ◽  
Rodyna A. Hosny
Keyword(s):  
Topological Spaces ◽  
Structure Space ◽  
Hereditary Class ◽  
The Family ◽  
Main Target ◽  
Whole Space ◽  
Weak Structure

Abstract Weak structure space (briefly, wss) has master looks, when the whole space is not open, and these classes of subsets are not closed under arbitrary unions and finite intersections, which classify it from typical topology. Our main target of this article is to introduce $$\psi _{{\mathcal {H}}}(.)$$ ψ H ( . ) -operator in hereditary class weak structure space (briefly, $${\mathcal {H}}wss$$ H w s s ) $$(X, w, {\mathcal {H}})$$ ( X , w , H ) and examine a number of its characteristics. Additionally, we clarify some relations that are credible in topological spaces but cannot be realized in generalized ones. As a generalization of w-open sets and w-semiopen sets, certain new kind of sets in a weak structure space via $$\psi _{{\mathcal {H}}}(.)$$ ψ H ( . ) -operator called $$\psi _{{\mathcal {H}}}$$ ψ H -semiopen sets are introduced. We prove that the family of $$\psi _{{\mathcal {H}}}$$ ψ H -semiopen sets composes a supra-topology on X. In view of hereditary class $${\mathcal {H}}_{0}$$ H 0 , $$w T_{1}$$ w T 1 -axiom is formulated and also some of their features are investigated.

scholarly journals nIαg-Compact spaces and nIαg-Lindelof spaces in nano ideal topological spaces

2020 ◽  
Author(s):  
M. Parimala ◽  
D. Arivuoli ◽  
R. Perumal ◽  
S. Krithika
Keyword(s):  
Topological Spaces ◽  
Compact Spaces

On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups

2003 ◽  
Vol 10 (2) ◽  
pp. 209-222
Author(s):  
I. Bakhia
Keyword(s):  
Wide Class ◽  
Sufficient Conditions ◽  
Topological Spaces ◽  
Topological Groups ◽  
Compact Spaces ◽  
Topological Semigroups

Abstract Functions of dimension modulo a (rather wide) class of spaces are considered and the conditions are found, under which the dimension of the product of spaces modulo these classes is equal to zero. Based on these results, the sufficient conditions are established, under which spaces of free topological semigroups (in the sense of Marxen) and spaces of free topological groups (in the sense of Markov and Graev) are zero-dimensional modulo classes of compact spaces.

scholarly journals A note on fragmentable topological spaces

1994 ◽  
Vol 49 (1) ◽  
pp. 91-100
Author(s):  
Toshihiro Nagamizu
Keyword(s):  
Topological Spaces ◽  
Compact Spaces

We extend the results of N.K. Ribarska and A.V. Arhangel'skiĭ to the class of strongly countably complete spaces. And we show another characterisation of Eberlein and Radon-Nikodým compact spaces.

scholarly journals Some classes of E-Compactness

1972 ◽  
Vol 13 (4) ◽  
pp. 492-500 ◽  
Author(s):  
Robert L. Blefko
Keyword(s):  
Closed Subset ◽  
Unit Interval ◽  
Related Question ◽  
Topological Spaces ◽  
Completely Regular ◽  
Compact Spaces

Mrowka and Engleking [1] have recently introduced a notion more general than that of compactness. Perhaps the most convenient direction at departure is the following: for spaces X and E, X is said to be E-compact if X is topologically embeddable as a closed subset of a product Em for some cardinal m, in which case we write X ⊂cl Em. More generally, X is said to be E-completely regular if X is topologically embeddable in a product Em for some m. For example, if we take E to be the unit interval I, we obtain the class of compact spaces and completely regular spaces, respectively, as is well-known. The question then arises, of course, given a space E, what spaces are compact with respect to it? A related question, to which we address ourselves in this note, is the following. Denote by K[E] all those topological spaces which are E-compact. Then we ask: are there very many distinct E-compact classes? It will develop that there are indeed quite a large number of such classes.

CONTINUITY ON GENERALISED TOPOLOGICAL SPACES VIA HEREDITARY CLASSES

2018 ◽  
Vol 97 (2) ◽  
pp. 320-330 ◽  
Author(s):  
P. MONTAGANTIRUD ◽  
W. THAIKUA
Keyword(s):  
Topological Spaces ◽  
Hereditary Class

A generalised topology is a collection of subsets of a given nonempty set containing the empty set and arbitrary unions of the elements in the collection. By using the concept of hereditary classes, a generalised topology can be extended to a new one, called a generalised topology via a hereditary class. We study continuity on generalised topological spaces via hereditary classes in various situations.

A note on λ-compact spaces

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
O. Karamzadeh ◽  
M. Namdari ◽  
M. Siavoshi
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Hausdorff Spaces ◽  
Compact Spaces

AbstractWe extend the well-known and important fact that “a topological space X is compact if and only if every ideal in C(X) is fixed”, to more general topological spaces. Some interesting consequences are also observed. In particular, the maximality of compact Hausdorff spaces with respect to the property of compactness is generalized and the topological spaces with this generalized property are characterized.

scholarly journals Soft Simply Compact Spaces

2020 ◽  
pp. 108-113
Author(s):  
S. Noori ◽  
Y. Y. Yousif
Keyword(s):  
Topological Spaces ◽  
Compact Spaces ◽  
Open Set ◽  
Separation Axioms

The aim of this research is to use the class of soft simply open set to define new types of separation axioms in soft topological spaces. We also introduce and study the concept of soft simply compactness.

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