scholarly journals β* - and β* - Connectedness

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Compact Space ◽  
General Topology ◽  
Topological Spaces ◽  
Connected Space ◽  
Fundamental Properties ◽  
Open Set ◽  
New Concepts

In 2014 Mubarki, Al-Rshudi, and Al-Juhani introduced and studied the notion of a set in general topology called β * - open sets and investigated its fundamental properties and studied the relationships between β * - open set and other topological sets including β * - continuity in topological spaces. The objective of this paper is to introduce the new concepts called β * - compact space, countably β * - compact space, β * - Lindelof space, almost β * - compact space, mildly β * - compact space and β * - connected space in general topology and investigate several properties and characterizations of these new concepts in topological spaces.

scholarly journals Infra -α- Compact and Infra -α- Connected Spaces

2021 ◽  
Vol 8 ◽  
pp. 41-57
Author(s):  
Raja Mohammad Latif
Keyword(s):  
Compact Space ◽  
General Topology ◽  
Topological Spaces ◽  
Connected Space ◽  
Fundamental Properties ◽  
Open Set ◽  
New Concepts ◽  
The Relationship ◽  
Connected Spaces

In 2016 Hakeem A. Othman and Md. Hanif Page introduced a new notion of set in general topology called an infra -α- open set and investigated its fundamental properties and studied the relationship between infra -α- open set and other topological sets. The objective of this paper is to introduce the new concepts called infra -α- compact space, countably infra -α- compact space, infra -α- Lindelof space, almost infra -α- compact space, mildly infra -α- compact space and infra -α- connected space in general topology and investigate several properties and characterizations of these new concepts in topological spaces.

scholarly journals Beta- Star- Continuity and Beta- Star- Contra- Continuity

2021 ◽  
Vol 7 ◽  
pp. 43-66
Author(s):  
Raja Mohammad Latif
Keyword(s):  
Continuous Functions ◽  
General Topology ◽  
Topological Spaces ◽  
New Class ◽  
Fundamental Properties ◽  
Open Set ◽  
Class Of Functions

In 2014 Mubarki, Al-Rshudi, and Al- Juhani introduced and studied the notion of a set in general topology called β*-open set and investigated its fundamental properties and studied the relationships between β*-open set and other topological sets including β*-continuity in topological spaces. We introduce and investigate several properties and characterizations of a new class of functions between topological spaces called β*- open, β*- closed, β*- continuous and β*- irresolute functions in topological spaces. We also introduce slightly β*- continuous, totally β*- continuous and almost β*- continuous functions between topological spaces and establish several characterizations of these new forms of functions. Furthermore, we also introduce and investigate certain ramifications of contra continuous and allied functions, namely, contra β*- continuous, and almost contra β*-continuous functions along with their several properties, characterizations and natural relationships. Moreover, we introduce new types of closed graphs by using β*- open sets and investigate its properties and characterizations in topological spaces.

scholarly journals ON An Infra-\(\alpha\)-Open Sets

2016 ◽  
Vol 4 (3) ◽  
pp. 12
Author(s):  
Hakeem Othman ◽  
Md.Hanif. Page
Keyword(s):  
General Topology ◽  
Connected Space ◽  
Basic Properties ◽  
New Class ◽  
Fundamental Properties ◽  
Open Set ◽  
Continuous Mappings

<p>In this paper, we define a new class of set in general topology called an infra- \(\alpha\) open set and we investigate fundamental properties by using this new class. The relation between infra-\(\alpha\)-open set and other topological sets are studied.</p><p>Moreover, In the light of this new definition, we also define some generalization of continuous mappings and discuss the relations between these new classes of mappings and other continuous mappings. Basic properties of these new mappings are studied and we apply these new classes to give characterization of connected space.</p>

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 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 Some properties of weak form of $\gamma$-semi-open sets

2012 ◽  
Vol 43 (3) ◽  
pp. 329-338
Author(s):  
Sabir Hussain ◽  
Mohammad Ahmad Alghamdi
Keyword(s):  
Decomposition Theorem ◽  
Weak Form ◽  
Topological Spaces ◽  
Basic Properties ◽  
Fundamental Properties ◽  
Open Set

In this paper, we introduce and explore fundamental properties of weak form of $\gamma$-semi-open sets namely maximal $\gamma$-semi-open sets in topological spaces such as decomposition theorem for maximal $\gamma$-semi-open set. Basic properties of intersection of maximal $\gamma$-semi-open sets are established, such as the $\gamma$-semi-closure law of $\gamma$-semi-radical.

scholarly journals Some Results in Neutrosophic Soft Topology Concerning Neutrosophic Soft ∗ b Open Sets

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Arif Mehmood ◽  
Saleem Abdullah ◽  
Mohammed M. Al-Shomrani ◽  
Muhammad Imran Khan ◽  
Orawit Thinnukool
Keyword(s):  
Compact Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Soft Topology ◽  
Open Set ◽  
Topological Features ◽  
Separation Axioms ◽  
Countable Space ◽  
Countably Compact

In this article, new generalised neutrosophic soft open known as neutrosophic soft ∗ b open set is introduced in neutrosophic soft topological spaces. Neutrosophic soft ∗ b open set is generated with the help of neutrosophic soft semiopen and neutrosophic soft preopen sets. Then, with the application of this new definition, some soft neutrosophical separation axioms, countability theorems, and countable space can be Hausdorff space under the subjection of neutrosophic soft sequence which is convergent, the cardinality of neutrosophic soft countable space, engagement of neutrosophic soft countable and uncountable spaces, neutrosophic soft topological features of the various spaces, soft neutrosophical continuity, the product of different soft neutrosophical spaces, and neutrosophic soft countably compact that has the characteristics of Bolzano Weierstrass Property (BVP) are studied. In addition to this, BVP shifting from one space to another through neutrosophic soft continuous functions, neutrosophic soft sequence convergence, and its marriage with neutrosophic soft compact space, sequentially compactness are addressed.

scholarly journals Bioperators on soft topological spaces

2021 ◽  
Vol 6 (11) ◽  
pp. 12471-12490
Author(s):  
Baravan A. Asaad ◽  
◽  
Tareq M. Al-shami ◽  
Abdelwaheb Mhemdi ◽  
◽  
...  
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
Fundamental Properties ◽  
Soft Topology ◽  
Open Set ◽  
Soft Topological Space

<abstract><p>To contribute to soft topology, we originate the notion of soft bioperators $ \tilde{\gamma} $ and $ {\tilde{\gamma}}^{'} $. Then, we apply them to analyze soft $ (\tilde{\gamma}, {\tilde{\gamma}}^{'}) $-open sets and study main properties. We also prove that every soft $ (\tilde{\gamma}, {\tilde{\gamma}}^{'}) $-open set is soft open; however, the converse is true only when the soft topological space is soft $ (\tilde{\gamma}, {\tilde{\gamma}}^{'}) $-regular. After that, we define and study two classes of soft closures namely $ Cl_{(\tilde{\gamma}, {\tilde{\gamma}}^{'})} $ and $ \tilde{\tau}_{(\tilde{\gamma}, {\tilde{\gamma}}^{'})} $-$ Cl $ operators, and two classes of soft interior namely $ Int_{(\tilde{\gamma}, {\tilde{\gamma}}^{'})} $ and $ \tilde{\tau}_{(\tilde{\gamma}, {\tilde{\gamma}}^{'})} $-$ Int $ operators. Moreover, we introduce the notions of soft $ (\tilde{\gamma}, {\tilde{\gamma}}^{'}) $-$ g $.closed sets and soft $ (\tilde{\gamma}, {\tilde{\gamma}}^{'}) $-$ T_{\frac{1}{2}} $ spaces, and explore their fundamental properties. In general, we explain the relationships between these notions, and give some counterexamples.</p></abstract>

Weak and strong forms of fuzzy \(\alpha\)-open (closed) sets and its applications

2018 ◽  
Vol 9 (2) ◽  
Author(s):  
Hakeem Ahmed Ali ◽  
Alanod M. Sibih
Keyword(s):  
Topological Spaces ◽  
Connected Space ◽  
Basic Properties ◽  
Closed Sets ◽  
Continuous Mappings ◽  
New Concepts ◽  
Fuzzy Topological Spaces ◽  
Closed Mappings

In this paper, we generalize the concept of infra-\(\alpha\)-open (closed) and supra-\(\alpha\)-open (closed) sets to fuzzy topological spaces and basic properties of these new concepts have been introduced. Some applications on fuzzy (supra-) infra-\(\alpha\)-open (closed) sets, likely, fuzzy (supra-) infra-\(\alpha\)-continuous mappings, fuzzy (supra-) infra-\(\alpha\)-open (closed) mappings, fuzzy supra-\(\alpha\)- irresolute mapping and fuzzy supra-\(\alpha\)-connected space are introduced. The relations and converse relations between these new concepts and others kinds of fuzzy open sets and fuzzy continuous mappings are discussed. Special results about these new concepts are investigated and studied.

Novel Idea of Gδ-α-Locally Continuous Functions

2021 ◽  
pp. 61-65
Author(s):  
R.Narmada Devi ◽  
Keyword(s):  
Continuous Function ◽  
Compact Space ◽  
Continuous Functions ◽  
Connected Space ◽  
Urysohn Space ◽  
Closed Sets ◽  
New Concepts ◽  
Locally Closed Sets

The new concepts of a neutrosophic Gδ set and neutrosophic Gδ-α-locally closed sets are introduced. Also, a neutrosophic εGδ-α-locally quasi neighborhood, neutrosophic Gδ-α-locally continuous function, neutrosophic Gδ-α-local T2 space, neutrosophic Gδ-α-local Urysohn space, neutrosophic Gδ-α-local connected space, and neutrosophic Gδ-α-local compact space are discussed and some interesting properties are established.

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