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 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 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 On spaces defined by Pytkeev networks

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 6115-6129 ◽  
Author(s):  
Xin Liu ◽  
Shou Lin
Keyword(s):  
Topological Space ◽  
Affirmative Answer ◽  
General Topology ◽  
Topological Spaces ◽  
Urysohn Space ◽  
Closed Mappings ◽  
The Relationship

The notions of networks and k-networks for topological spaces have played an important role in general topology. Pytkeev networks, strict Pytkeev networks and cn-networks for topological spaces are defined by T. Banakh, and S. Gabriyelyan and J. K?kol, respectively. In this paper, we discuss the relationship among certain Pytkeev networks, strict Pytkeev networks, cn-networks and k-networks in a topological space, and detect their operational properties. It is proved that every point-countable Pytkeev network for a topological space is a quasi-k-network, and every topological space with a point-countable cn-network is a meta-Lindel?f D-space, which give an affirmative answer to the following problem [25, 29]: Is every Fr?chet-Urysohn space with a pointcountable cs'-network a meta-Lindel?f space? Some mapping theorems on the spaces with certain Pytkeev networks are established and it is showed that (strict) Pytkeev networks are preserved by closed mappings and finite-to-one pseudo-open mappings, and cn-networks are preserved by pseudo-open mappings, in particular, spaces with a point-countable Pytkeev network are preserved by closed mappings.

scholarly journals Pythagorean Fuzzy Rough Connected Spaces

2021 ◽  
Vol 2070 (1) ◽  
pp. 012069
Author(s):  
P Revathi ◽  
R Radhamani
Keyword(s):  
Rough Set ◽  
Topological Spaces ◽  
Connected Space ◽  
Fuzzy Rough Set ◽  
Connected Spaces

Abstract In this paper Pythagorean fuzzy rough set and Pythagorean fuzzy rough topological spaces are defined for the connected space. Then, the properties of connectedness are discussed with examples.

scholarly journals Remarks on soft omega-closed sets in soft topological spaces

2014 ◽  
Vol 33 (1) ◽  
pp. 181
Author(s):  
Nirmala Rebecca Paul
Keyword(s):  
Compact Space ◽  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
The Relationship

The paper introduces soft omega-closed sets in soft topological spaces and establishes the relationship between other existing generlised closed sets in soft topological spaces. It derives the basic properties of soft omega-closed sets. As an application it proves that a soft omega-closed set in a soft compact space is soft compact.

scholarly journals Certain Concepts by Using ωpre-Open Sets

2019 ◽  
Vol 54 (6) ◽  
Author(s):  
Kasim Abbas Hussain ◽  
Haider Jebur Ali ◽  
Alaa Malik Soady
Keyword(s):  
Compact Space ◽  
Continuous Functions ◽  
Regular Space ◽  
Continuous Image ◽  
Open Set ◽  
The Relationship

The aim of this paper is to add new types of continuous functions and results in the specialization field, where we merge two important terms of open sets that are pre-open and ω-open to get a new set named ωp-open set, where we introduce new functions by using this set, such as Mωpc, ωpMc, ωpMωpc, ωp-continuous, ωp*-continuous, and ωp-irresolute function. We clarify the relationship between these types and illustrate their relationship with some other types of continuous functions. Also we define some new types of spaces such as, ωp-compact, ωp-Lindelöf, and Cωp-Lindelöf. In addition, we submit important results like, the ωp*-continuous image of compact space being ωp-compact, and if X is a ωp-regular space, hence it is Cωp-Lindelöf, as well as we provide the composition between most of the new functions that we defined. Many other results have been found in this our work and they are supported by many examples.

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.

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