scholarly journals e#-open and *e-open sets via -open sets

2021 ◽  
Vol 12 (2) ◽  
pp. 2125-2128
Author(s):  
V. Amsaveni, Et. al.
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closure Operators ◽  
Closed Sets

The notion of -open sets in a topological space was studied by Velicko.  Usha Parmeshwari et.al. and Indira et.al. introduced the concepts of b# and *b open sets respectively. Following this Ekici et. al. studied the notions of e-open and e-closed sets by mixing the closure, interior, -interior and -closure operators.  In this paper some new sets namely e#-open and *e-open sets are defined and their relationship with other similar concetps in topological spaces will be investigated.

scholarly journals New Soft Structure: Infra Soft Topological Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Tareq M. Al-shami
Keyword(s):  
Topological Space ◽  
Soft Set ◽  
Topological Spaces ◽  
Closure Operators ◽  
Relative Topology ◽  
Closed Sets ◽  
Soft Topology ◽  
Soft Limit ◽  
Basic Concepts ◽  
Soft Topological Space

It is always convenient to find the weakest conditions that preserve some topologically inspired properties. To this end, we introduce the concept of an infra soft topology which is a collection of subsets that extend the concept of soft topology by dispensing with the postulate that the collection is closed under arbitrary unions. We study the basic concepts of infra soft topological spaces such as infra soft open and infra soft closed sets, infra soft interior and infra soft closure operators, and infra soft limit and infra soft boundary points of a soft set. We reveal the main properties of these concepts with the help of some elucidative examples. Then, we present some methods to generate infra soft topologies such as infra soft neighbourhood systems, basis of infra soft topology, and infra soft relative topology. We also investigate how we initiate an infra soft topology from crisp infra topologies. In the end, we explore the concept of continuity between infra soft topological spaces and determine the conditions under which the continuity is preserved between infra soft topological space and its parametric infra topological spaces.

scholarly journals Soft Semi ω-Open Sets

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3168
Author(s):  
Samer Al Ghour
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closure Operators ◽  
Closed Sets ◽  
Soft Topology ◽  
Locally Countable ◽  
Soft Topological Space

In this paper, we introduce the class of soft semi ω-open sets of a soft topological space (X,τ,A), using soft ω-open sets. We show that the class of soft semi ω-open sets contains both the soft topology τω and the class of soft semi-open sets. Additionally, we define soft semi ω-closed sets as the class of soft complements of soft semi ω-open sets. We present here a study of the properties of soft semi ω-open sets, especially in (X,τ,A) and (X,τω,A). In particular, we prove that the class of soft semi ω-open sets is closed under arbitrary soft union but not closed under finite soft intersections; we also study the correspondence between the soft topology of soft semi ω-open sets of a soft topological space and their generated topological spaces and vice versa. In addition to these, we introduce the soft semi ω-interior and soft semi ω-closure operators via soft semi ω-open and soft semi ω-closed sets. We prove several equations regarding these two new soft operators. In particular, we prove that these operators can be calculated using other usual soft operators in both of (X,τ,A) and (X,τω,A), and some equations focus on soft anti-locally countable soft topological spaces.

Neutrosophic Nano Ideal Topological Structures

2018 ◽  
Author(s):  
Parimala Mani ◽  
Karthika M ◽  
jafari S ◽  
Smarandache F ◽  
Ramalingam Udhayakumar
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Structures ◽  
Basic Properties ◽  
Closed Sets ◽  
Structural Space ◽  
New Type

Neutrosophic nano topology and Nano ideal topological spaces induced the authors to propose this new concept. The aim of this paper is to introduce a new type of structural space called neutrosophic nano ideal topological spaces and investigate the relation between neutrosophic nano topological space and neutrosophic nano ideal topological spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.

scholarly journals Neighbourhood lattices – a poset approach to topological spaces

1989 ◽  
Vol 39 (1) ◽  
pp. 31-48 ◽  
Author(s):  
Frank P. Prokop
Keyword(s):  
Topological Space ◽  
Lattice Structure ◽  
Algebraic Closure ◽  
Topological Spaces ◽  
Closure Operators ◽  
Continuity Properties ◽  
Image Function ◽  
Topological Closure ◽  
Arbitrary Lattice ◽  
The Relationship

In this paper neighbourhood lattices are developed as a generalisation of topological spaces in order to examine to what extent the concepts of “openness”, “closedness”, and “continuity” defined in topological spaces depend on the lattice structure of P(X), the power set of X.A general pre-neighbourhood system, which satisfies the poset analogues of the neighbourhood system of points in a topological space, is defined on an ∧-semi-lattice, and is used to define open elements. Neighbourhood systems, which satisfy the poset analogues of the neighbourhood system of sets in a topological space, are introduced and it is shown that it is the conditionally complete atomistic structure of P(X) which determines the extension of pre-neighbourhoods of points to the neighbourhoods of sets.The duals of pre-neighbourhood systems are used to generate closed elements in an arbitrary lattice, independently of closure operators or complementation. These dual systems then form the backdrop for a brief discussion of the relationship between preneighbourhood systems, topological closure operators, algebraic closure operators, and Čech closure operators.Continuity is defined for functions between neighbourhood lattices, and it is proved that a function f: X → Y between topological spaces is continuous if and only if corresponding direct image function between the neighbourhood lattices P(X) and P(Y) is continuous in the neighbourhood sense. Further, it is shown that the algebraic character of continuity, that is, the non-convergence aspects, depends only on the properites of pre-neighbourhood systems. This observation leads to a discussion of the continuity properties of residuated mappings. Finally, the topological properties of normality and regularity are characterised in terms of the continuity properties of the closure operator on a topological space.

Δμ-sets and ∇μ-sets in generalized topological spaces

2017 ◽  
Vol 24 (3) ◽  
pp. 403-407
Author(s):  
Pon Jeyanthi ◽  
Periadurai Nalayini ◽  
Takashi Noiri
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
Generalized Topological Space

AbstractIn this paper, we introduce and study some properties of the sets, namely {\Delta_{\mu}}-sets, {\nabla_{\mu}}-sets and {\Delta_{\mu}^{*}}-closed sets in a generalized topological space.

scholarly journals Theory of g-Tg-Interior and g-Tg-Closure Operators: Definitions, Essential Properties, and Commutativity

2019 ◽  
Author(s):  
Mohammad Irshad KHODABOCUS ◽  
Noor-Ul-Hacq SOOKIA
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closure Operators ◽  
New Class ◽  
Essential Properties ◽  
Generalized Topological Space ◽  
Outstanding Result

In a generalized topological space Tg = (Ω, Tg), ordinary interior and ordinary closure operators intg, clg : P (Ω) −→ P (Ω), respectively, are defined in terms of ordinary sets. In order to let these operators be as general and unified a manner as possible, and so to prove as many generalized forms of some of the most important theorems in generalized topological spaces as possible, thereby attaining desirable and interesting results, the present au- thors have defined the notions of generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in terms of a new class of generalized sets which they studied earlier and studied their essen- tial properties and commutativity. The outstanding result to which the study has led to is: g-Intg : P (Ω) −→ P (Ω) is finer (or, larger, stronger) than intg : P (Ω) −→ P (Ω) and g-Clg : P (Ω) −→ P (Ω) is coarser (or, smal ler, weaker) than clg : P (Ω) −→ P (Ω). The elements supporting this fact are reported therein as a source of inspiration for more generalized operations.

scholarly journals Fine Fuzzy sp Closed Sets in Fine Fuzzy Topological Spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 1306-1313
Keyword(s):  
Continuous Function ◽  
Topological Space ◽  
Inverse Image ◽  
Continuous Functions ◽  
Topological Spaces ◽  
The Novel ◽  
Closed Set ◽  
Closed Sets ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

The main view of this article is the extended version of the fine topological space to the novel kind of space say fine fuzzy topological space which is developed by the notion called collection of quasi coincident of fuzzy sets. In this connection, fine fuzzy closed sets are introduced and studied some features on it. Further, the relationship between fine fuzzy closed sets with certain types of fine fuzzy closed sets are investigated and their converses need not be true are elucidated with necessary examples. Fine fuzzy continuous function is defined as the inverse image of fine fuzzy closed set is fine fuzzy closed and its interrelations with other types of fine fuzzy continuous functions are obtained. The reverse implication need not be true is proven with examples. Finally, the applications of fine fuzzy continuous function are explained by using the composition.

scholarly journals Relations of Pre Generalized Regular Weakly Locally Closed Sets in Topological Spaces

2021 ◽  
Vol 12 (3) ◽  
pp. 3444-3454
Author(s):  
Vijayakumari T Et.al
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Set ◽  
Closed Sets ◽  
Open Set ◽  
Continuous Maps ◽  
Locally Closed Sets

In this paper pgrw-locally closed set, pgrw-locally closed*-set and pgrw-locally closed**-set are introduced. A subset A of a topological space (X,t) is called pgrw-locally closed (pgrw-lc) if A=GÇF where G is a pgrw-open set and F is a pgrw-closed set in (X,t). A subset A of a topological space (X,t) is a pgrw-lc* set if there exist a pgrw-open set G and a closed set F in X such that A= GÇF. A subset A of a topological space (X,t) is a pgrw-lc**-set if there exists an open set G and a pgrw-closed set F such that A=GÇF. The results regarding pgrw-locally closed sets, pgrw-locally closed* sets, pgrw-locally closed** sets, pgrw-lc-continuous maps and pgrw-lc-irresolute maps and some of the properties of these sets and their relation with other lc-sets are established.

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.

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