scholarly journals Hereditary properties of semi-separation axioms and their applications

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4689-4700 ◽  
Author(s):  
Sang-Eon Han
Keyword(s):  
Topological Space ◽  
Infinite Product ◽  
Topological Spaces ◽  
Hereditary Property ◽  
Separation Axiom ◽  
Product Property ◽  
Low Level ◽  
Separation Axioms ◽  
Hereditary Properties

The paper studies the open-hereditary property of semi-separation axioms and applies it to the study of digital topological spaces such as an n-dimensional Khalimsky topological space, a Marcus-Wyse topological space and so on. More precisely, we study various properties of digital topological spaces related to low-level and semi-separation axioms such as T1/2 , semi-T1/2 , semi-T1, semi-T2, etc. Besides, using the finite or the infinite product property of the semi-Ti-separation axiom, i ? {1,2}, we prove that the n-dimensional Khalimsky topological space is a semi-T2-space. After showing that not every subspace of the digital topological spaces satisfies the semi-Ti-separation axiom, i ?{1,2}, we prove that the semi-Tiseparation property is open-hereditary, i ? {1,2}. All spaces in the paper are assumed to be nonempty and connected.

scholarly journals Some new separation axioms in fuzzy soft topological spaces

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1775-1783
Author(s):  
Islam Taha
Keyword(s):  
Topological Space ◽  
Topological Property ◽  
Topological Spaces ◽  
Hereditary Property ◽  
Invariance Properties ◽  
Separation Axioms ◽  
New Form ◽  
Soft Topological Space

In this paper, a new form of separation axioms called r-fuzzy soft Ti;(i = 0,1,2,3,4), r-fuzzy soft regular and r-fuzzy soft normal axioms are introduced in a fuzzy soft topological space based on the paper Ayg?no?lu et al. [7]. Also, the relations of these axioms with each other are investigated with the help of examples. Furthermore, some fuzzy soft invariance properties, namely fuzzy soft topological property and hereditary property are specified.

scholarly journals Separation Axioms in Intuitionistic Fuzzy Topological Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Amit Kumar Singh ◽  
Rekha Srivastava
Keyword(s):  
Topological Space ◽  
Left Adjoint ◽  
Topological Spaces ◽  
Intuitionistic Fuzzy ◽  
Separation Axioms ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

In this paper we have studied separation axiomsTi,i=0,1,2in an intuitionistic fuzzy topological space introduced by Coker. We also show the existence of functorsℬ:IF-Top→BF-Topand𝒟:BF-Top→IF-Topand observe that𝒟is left adjoint toℬ.

scholarly journals Fuzzyθ-closure operator on fuzzy topological spaces

1991 ◽  
Vol 14 (2) ◽  
pp. 309-314 ◽  
Author(s):  
M. N. Mukherjee ◽  
S. P. Sinha
Keyword(s):  
Topological Space ◽  
Fuzzy Sets ◽  
Closure Operator ◽  
Topological Spaces ◽  
Separation Axioms ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

The paper contains a study of fuzzyθ-closure operator,θ-closures of fuzzy sets in a fuzzy topological space are characterized and some of their properties along with their relation with fuzzyδ-closures are investigated. As applications of these concepts, certain functions as well as some spaces satisfying certain fuzzy separation axioms are characterized in terms of fuzzyθ-closures andδ-closures.

scholarly journals A Class of Separation Axioms in Generalized Topology

2016 ◽  
Vol 4 (2) ◽  
pp. 151-159
Author(s):  
D Anabalan ◽  
Santhi C
Keyword(s):  
Topological Space ◽  
Generalized Topology ◽  
Regular Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
New Class ◽  
Separation Axioms ◽  
Generalized Topological Space

The purpose of this paper is to introduce and study some new class of definitions like µ-point closure and gµ –regular space concerning generalized topological space. We obtain some characterizations and several properties of such definitions. This paper takes some investigations on generalized topological spaces with gµ –closed sets and gµ–closed sets.

A note on nano g #α-closed maps in nano topological spaces

2020 ◽  
pp. 539-548
Author(s):  
S. Visagapriya ◽  
V. Kokilavani
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
Separation Axioms

The point of this article is to show separation axioms of Nano $g^{\#} \alpha$ closed sets in nano topological space. We moreover present and explore nano $g^{\#} \alpha$-closed maps and additionally consider their principal properties.

On ΛIs-sets and the related notions in ideal topological spaces

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
José Sanabria ◽  
Ennis Rosas ◽  
Carlos Carpintero
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
Separation Axioms

AbstractIn this paper, we define and study the notions of ΛIs-sets, ΛIs-closed sets and I-generalized semi-closed (briefly I-gs-closed) sets by using semi-I-open sets in an ideal topological space. Moreover, we present and characterize two new low separation axioms using the above notions.

scholarly journals On certain types of sets in ideal topological spaces

2015 ◽  
Vol 53 (2) ◽  
pp. 99-108
Author(s):  
Dhananjoy Mandal ◽  
M. N. Mukherjee
Keyword(s):  
Topological Space ◽  
Present Article ◽  
Topological Spaces ◽  
Separation Axiom

Abstract In the present article we introduce certain typical sets in an ideal topological space, some such corresponding versions in topological spaces being already there in the literature. We prove several properties of the introduced classes of sets, and finally as application, we initiate the study of a kind of separation axiom, termed $* - T_{{1 \over 2}}$ -property.

Some regular generalized star b-separation axiom in bigeneralized topological spaces

2017 ◽  
Vol 11 (01) ◽  
pp. 1850010
Author(s):  
Josephine Josol Baculta ◽  
Helen Moso Rara
Keyword(s):  
Topological Spaces ◽  
Separation Axiom ◽  
Separation Axioms

The purpose of this paper is to introduce and investigate some [Formula: see text] separation axioms in bigeneralized topological spaces. Using the concepts of regular generalized star b-open sets due to Indirani and Sindhu, the study defines and characterizes [Formula: see text]-[Formula: see text], [Formula: see text]-[Formula: see text], [Formula: see text]-regular and [Formula: see text]-normal spaces.

scholarly journals CLOSURES IN FORMAL LANGUAGES AND KURATOWSKI'S THEOREM

2011 ◽  
Vol 22 (02) ◽  
pp. 301-321 ◽  
Author(s):  
JANUSZ BRZOZOWSKI ◽  
ELYOT GRANT ◽  
JEFFREY SHALLIT
Keyword(s):  
Topological Space ◽  
Formal Languages ◽  
Topological Spaces ◽  
Famous Theorem ◽  
Separation Axioms ◽  
Kleene Closure

A famous theorem of Kuratowski states that, in a topological space, at most 14 distinct sets can be produced by repeatedly applying the operations of closure and complement to a given set. We re-examine this theorem in the setting of formal languages, where by "closure" we mean either Kleene closure or positive closure. We classify languages according to the structure of the algebras they generate under iterations of complement and closure. There are precisely 9 such algebras in the case of positive closure, and 12 in the case of Kleene closure. We study how the properties of being open and closed are preserved under concatenation. We investigate analogues, in formal languages, of the separation axioms in topological spaces; one of our main results is that there is a clopen partition separating two words if and only if the words do not commute. We can decide in quadratic time if the language specified by a DFA is closed, but if the language is specified by an NFA, the problem is PSPACE-complete.

scholarly journals Pre Separation Axioms In Neutrosophic Crisp Topological Spaces

2020 ◽  
pp. 72-79
Author(s):  
Riad K. Al Al-Hamido ◽  
◽  
◽  
◽  
Luai Salha ◽  
...  
Keyword(s):  
Topological Space ◽  
The Other ◽  
Topological Spaces ◽  
Open Set ◽  
Separation Axioms ◽  
New Type

In this paper, A new type of separation axioms in the neutrosophic crisp Topological space named neutrosophic crisp pre separation axioms is going to be defined , in which neutrosophic crisp pre open set and neutrosophic crisp point are to be depended on. Also, relations among them and the other type are going to be found.

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