scholarly journals \mu-\mu^{*} - Connectedness via Hereditary Classes

2013 ◽  
Vol 33 (1) ◽  
pp. 41
Author(s):  
Shyamapada Modak
Keyword(s):  
Topological Spaces ◽  
Hereditary Class ◽  
Connected Sets ◽  
Connected Set ◽  
Separated Sets

This paper is an attempt to study and introduce the notion of - - connected set in generalized topological spaces with a hereditary class. We have also investigate the relationships between -separated sets, s - connected sets, c -I - connected sets, c -c -connected sets, c-I - connected sets, -I - connected sets. Further we give some representations of the above connected sets via (-0) - continuity and (-0) - openness.

scholarly journals Weakly chain separated sets in a topological space

2021 ◽  
Vol 52 ◽  
pp. 5-16
Author(s):  
Nikita Shekutkovski ◽  
Zoran Misajleski ◽  
Aneta Velkoska ◽  
Emin Durmishi
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Connected Sets ◽  
Connected Set ◽  
Separated Sets ◽  
Better Than

In this paper we introduce the notion of pair of weakly chain separated sets in a topological space. If two sets are chain separated in the topological space, then they are weakly chain separated in the same space. We give an example of weakly chain separated sets in a topological space that are not chain separated in the space. Then we study the properties of these sets. Also we mention the criteria for two kind of topological spaces by using the notion of chain. The topological space is totally separated if and only if any two different singletons (unit subsets) are weakly chain separated in the space, and it is the discrete if and only if any pair of different nonempty subsets are chain separated. Moreover we give a criterion for chain connected set in a topological space by using the notion of weakly chain separateness. This criterion seems to be better than the criterion of chain connectedness by using the notion of pair of chain separated sets. Then we prove the properties of chain connected, and as a consequence of connected sets in a topological space by using the notion of weakly chain separateness.

scholarly journals Generalized Fuzzy Soft Connected Sets in Generalized Fuzzy Soft Topological Spaces

2018 ◽  
Vol 14 (2) ◽  
pp. 7787-7805
Author(s):  
Mohammed Saleh Malfi ◽  
Fathi Hishem Khedr ◽  
Mohamad Azab Abd Allah
Keyword(s):  
Topological Spaces ◽  
Connected Sets ◽  
Separated Sets ◽  
The Relationship

In this paper we introduce some types of generalized fuzzy soft separated sets and study some of their properties. Next, the notion of connectedness in fuzzy soft topological spaces due to Karata et al, Mahanta et al, and Kandil  et al., extended to generalized fuzzy soft topological spaces. The relationship between these types of connectedness in generalized fuzzy soft topological spaces is investigated with the help of number of counter examples.

scholarly journals Fuzzy Soft Connected Sets in Fuzzy Soft Topological Spaces

2016 ◽  
Vol 12 (8) ◽  
pp. 6473-6888 ◽  
Author(s):  
A Kandil ◽  
O. A. E Tantawy
Keyword(s):  
Topological Spaces ◽  
Connected Sets ◽  
Fuzzy Topological Spaces ◽  
Separated Sets ◽  
The Relationship

In this paper we introduce some types of fuzzy soft separated sets and study some of thier preperties. Next, the notion of connectedness in fuzzy topological spaces due to Ming and Ming, Zheng etc., extended to fuzzy soft topological spaces. The relationship between these types of connectedness in fuzzy soft topological spaces is investigated with the help of number of counter examples.

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 \mu - k - Connectedness in GTS

2014 ◽  
Vol 33 (2) ◽  
pp. 161-165
Author(s):  
Shyamapada Modak ◽  
Takashi Noiri
Keyword(s):  
Connected Sets ◽  
Separated Sets

Csaszar [4] introduced \mu - semi - open sets, \mu - preopen sets, \mu - \alpha - open sets and \mu - \beta - open sets in a GTS (X, \tau). By using the \mu - \sigma - closure, \mu - \pi - closure, \mu - \alpha - closure and \mu - \beta - closure in (X, \tau), we introduce and investigate the notions \mu - k - separated sets and \mu - k - connected sets in (X, \tau).

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.

scholarly journals Fuzzy soft connected sets in fuzzy soft topological spaces II

2017 ◽  
Vol 25 (2) ◽  
pp. 171-177 ◽  
Author(s):  
A. Kandil ◽  
O.A. El-Tantawy ◽  
S.A. El-Sheikh ◽  
Sawsan S.S. El-Sayed
Keyword(s):  
Topological Spaces ◽  
Connected Sets

scholarly journals On β-Open Sets and Ideals in Topological Spaces

2019 ◽  
Vol 12 (3) ◽  
pp. 893-905
Author(s):  
Glaisa T. Catalan ◽  
Roberto N. Padua ◽  
Michael Jr. Patula Baldado
Keyword(s):  
Topological Space ◽  
Compact Space ◽  
Topological Spaces ◽  
Open Set ◽  
Separated Sets ◽  
The Ideal

Let X be a topological space and I be an ideal in X. A subset A of a topological space X is called a β-open set if A ⊆ cl(int(cl(A))). A subset A of X is called β-open with respect to the ideal I, or βI -open, if there exists an open set U such that (1) U − A ∈ I, and (2) A − cl(int(cl(U))) ∈ I. A space X is said to be a βI -compact space if it is βI -compact as a subset. An ideal topological space (X, τ, I) is said to be a cβI -compact space if it is cβI -compact as a subset. An ideal topological space (X, τ, I) is said to be a countably βI -compact space if X is countably βI -compact as a subset. Two sets A and B in an ideal topological space (X, τ, I) is said to be βI -separated if clβI (A) ∩ B = ∅ = A ∩ clβ(B). A subset A of an ideal topological space (X, τ, I) is said to be βI -connected if it cannot be expressed as a union of two βI -separated sets. An ideal topological space (X, τ, I) is said to be βI -connected if X βI -connected as a subset. In this study, we introduced the notions βI -open set, βI -compact, cβI -compact, βI -hyperconnected, cβI -hyperconnected, βI -connected and βI -separated. Moreover, we investigated the concept β-open set by determining some of its properties relative to the above-mentioned notions.

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.

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