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 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 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.

ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Open Set ◽  
Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

scholarly journals Some properties of maximal open sets

2003 ◽  
Vol 2003 (21) ◽  
pp. 1331-1340 ◽  
Author(s):  
Fumie Nakaoka ◽  
Nobuyuki Oda
Keyword(s):  
Decomposition Theorem ◽  
Basic Properties ◽  
Fundamental Properties ◽  
Open Set ◽  
The Law

Some fundamental properties of maximal open sets are obtained, such as decomposition theorem for a maximal open set. Basic properties of intersections of maximal open sets are established, such as the law of radical closure.

scholarly journals Quasi cl-supercontinuous functions and their function spaces

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
J. K. Kohli ◽  
Jeetendra Aggarwal
Keyword(s):  
Continuous Functions ◽  
Function Spaces ◽  
Strong Form ◽  
General Topology ◽  
Regular Space ◽  
Basic Properties ◽  
New Class ◽  
Mathematical Literature ◽  
Class Of Functions ◽  
Appl Math

AbstractA new class of functions called ‘quasi cl-supercontinuous functions’ is introduced. Basic properties of quasi cl-supercontinuous functions are studied and their place in the hierarchy of variants of continuity that already exist in the mathematical literature is elaborated. The notion of quasi cl-supercontinuity, in general, is independent of continuity but coincides with cl-supercontinuity (≡ clopen continuity) (Applied General Topology 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772), a significantly strong form of continuity, if range is a regular space. The class of quasi cl-supercontinuous functions properly contains each of the classes of (i) quasi perfectly continuous functions and (ii) almost cl-supercontinuous functions; and is strictly contained in the class of quasi

A View on Fuzzy Minimal Open Sets and Fuzzy Maximal Open Sets

2015 ◽  
Vol 7 (1) ◽  
pp. 62-73 ◽  
Author(s):  
Hamid Reza Moradi
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Basic Properties ◽  
New Class ◽  
Properties And Characterization ◽  
Open Set ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Characterization Theorems

A nonzero fuzzy open set () of a fuzzy topological space is said to be fuzzy minimal open (resp. fuzzy maximal open) set if any fuzzy open set which is contained (resp. contains) in is either or itself (resp. either or itself). In this note, a new class of sets called fuzzy minimal open sets and fuzzy maximal open sets in fuzzy topological spaces are introduced and studied which are subclasses of open sets. Some basic properties and characterization theorems are also to be investigated.

scholarly journals Remarks on Pre-I-Regular Pre-I-Open Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
R. Sajuntha
Keyword(s):  
Equivalence Relation ◽  
Closed Sets ◽  
New Class ◽  
Fundamental Properties ◽  
Open Set ◽  
Regular Sets

We deal with the new class of pre-I-regular pre-I-open sets in which the notion of pre-I-open set is involved. We characterize these sets and study some of their fundamental properties. We also present other notions called extremally pre-I-disconnectedness, locally pre-I-indiscreetness, and pre-I-regular sets by utilizing the notion of pre-I-open and pre-I-closed sets by which we obtain some equivalence relation for pre-I-regular pre-I-open sets.

scholarly journals Neutrosophic soft δ-topology and neutrosophic soft δ-compactness

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3441-3458
Author(s):  
Ahu Acikgoz ◽  
Ferhat Esenbel
Keyword(s):  
Basic Properties ◽  
Soft Topology ◽  
Open Set ◽  
Continuous Mappings ◽  
Regular Open

We introduce the concepts of neutrosophic soft ?-interior, neutrosophic soft quasi-coincidence, neutrosophic soft q-neighbourhood, neutrosophic soft regular open set, neutrosophic soft ?-closure, neutrosophic soft ?-closure and neutrosophic soft semi open set. It is also shown that the set of all neutrosophic soft ?-open sets is a neutrosophic soft topology, which is called the neutrosophic soft ?-topology. We obtain equivalent forms of neutrosophic soft ?-continuity. Moreover, the notions of neutrosophic soft ?-compactness and neutrosophic soft locally ?-compactness are defined and their basic properties under neutrosophic soft ?-continuous mappings are investigated.

\(\alpha_\beta\)-Connectedness as a characterization of connectedness

2018 ◽  
Vol 9 (2) ◽  
pp. 119-129 ◽  
Author(s):  
B. K. Tyagi ◽  
Manoj Bhardwaj ◽  
Sumit Singh
Keyword(s):  
Topological Space ◽  
Intermediate Value Theorem ◽  
New Class ◽  
Continuous Mappings ◽  
Intermediate Value ◽  
Connected Spaces

In this paper, a new class of \(\alpha_\beta\)-open sets in a topological space \(X\) is introduced which forms a topology on \(X\). The connectedness of this new topology on \(X\), called \(\alpha_\beta\)-connectedness, turns out to be equivalent to connectedness of \(X\) and hence also to \(\alpha\)-connectedness of \(X\). The \(\alpha_\beta\)-continuous and \(\alpha_\beta\)-irresolute mappings are defined and their relationship with other mappings such as continuous mappings and \(\alpha\)-continuous mappings are discussed. An intermediate value theorem is obtained. The hyperconnected spaces constitute a subclass of \(\alpha_\beta\)-connected spaces.

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