scholarly journals On Slight Omega Continuity and Irresoluteness between Generalized Topological Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 780
Author(s):  
Samer Al Ghour ◽  
Abeer Al-Nimer
Keyword(s):  
Topological Spaces ◽  
Countable Compactness ◽  
Class Of Functions

We introduce slightly ω - ( μ 1 , μ 2 ) -continuous and slightly ω - ( μ 1 , μ 2 ) -irresolute functions as two new classes of functions on generalized topological spaces. We obtained several properties and characterizations of these functions. Moreover, we deal with preservations of Lindelofness, mild Lindelofness, mildly countable compactness, and connectedness under images or inverse images of a class of functions, which gives symmetric relationships.

scholarly journals A note on weakly θ-continuous functions

1989 ◽  
Vol 12 (1) ◽  
pp. 9-13 ◽  
Author(s):  
M. Mrševic ◽  
I. L. Reilly
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
Topological Spaces ◽  
New Class ◽  
Weakly Continuous ◽  
Class Of Functions

Recently a new class of functions between topological spaces, called weaklyθ-continuous functions, has been introduced and studied. In this paper we show how an appropriate change of topology on the domain of a weaklyθ-continuous function reduces it to a weakly continuous function. This paper examines some of the consequences of this result.

scholarly journals On weakly BR-open functions and their characterizations in topological spaces

2011 ◽  
Vol 44 (1) ◽  
Author(s):  
M. Caldas ◽  
E. Ekici ◽  
S. Jafari ◽  
R. M. Latif
Keyword(s):  
Topological Spaces ◽  
New Class ◽  
Class Of Functions

AbstractIn this paper, we introduce and study a new class of functions by using the notions of b-

scholarly journals Fuzzy Inverse Compactness

2008 ◽  
Vol 2008 ◽  
pp. 1-9
Author(s):  
Halis Aygün ◽  
A. Arzu Bural ◽  
S. R. T. Kudri
Keyword(s):  
Fuzzy Sets ◽  
Topological Spaces ◽  
Countable Compactness ◽  
Fuzzy Topological Spaces

We introduce definitions of fuzzy inverse compactness, fuzzy inverse countable compactness, and fuzzy inverse Lindelöfness on arbitrary -fuzzy sets in -fuzzy topological spaces. We prove that the proposed definitions are good extensions of the corresponding concepts in ordinary topology and obtain different characterizations of fuzzy inverse compactness.

scholarly journals Measurement of Countable Compactness and Lindelöf Property in RL -Fuzzy Topological Spaces

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Xiongwei Zhang ◽  
Ibtesam Alshammari ◽  
A. Ghareeb
Keyword(s):  
Distributive Lattice ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Implication Operator ◽  
Completely Distributive ◽  
Countable Compactness ◽  
Definition Of ◽  
Fuzzy Topological Spaces ◽  
Completely Distributive Lattice ◽  
Special Case

Based on the concepts of pseudocomplement of L -subsets and the implication operator where L is a completely distributive lattice with order-reversing involution, the definition of countable RL -fuzzy compactness degree and the Lindelöf property degree of an L -subset in RL -fuzzy topology are introduced and characterized. Since L -fuzzy topology in the sense of Kubiak and Šostak is a special case of RL -fuzzy topology, the degrees of RL -fuzzy compactness and the Lindelöf property are generalizations of the corresponding degrees in L -fuzzy topology.

scholarly journals On Maximal and Minimal Sets in Topological Spaces

2019 ◽  
Vol 54 (6) ◽  
Author(s):  
Raad Aziz Hussain Al-Abdulla
Keyword(s):  
Topological Spaces ◽  
Minimal Sets ◽  
Class Of Functions

In this paper, we examine new classes of sets in topological spaces that are called maximal and minimal sets. Their relations are introduced and studied. Also, a recent class of functions has been found in topological spaces which use maximal and minimal sets. In addition, maximal and minimal sets are independent; the maximal and minimal sets cannot be equivalent under any conditions.

scholarly journals On some types of functions and a form of compactness via $ \omega _{s} $-open sets

2021 ◽  
Vol 7 (2) ◽  
pp. 2220-2236
Author(s):  
Samer Al Ghour ◽  
Keyword(s):  
Sufficient Conditions ◽  
Strong Form ◽  
Topological Spaces ◽  
New Class ◽  
Locally Countable ◽  
Class Of Functions

<abstract><p>In this paper, $ \omega _{s} $-irresoluteness as a strong form of $ \omega _{s} $-continuity is introduced. It is proved that $ \omega _{s} $-irresoluteness is independent of each of continuity and irresoluteness. Also, $ \omega _{s} $-openness which lies strictly between openness and semi-openness is defined. Sufficient conditions for the equivalence between $ \omega _{s} $-openness and openness, and between $ \omega _{s} $-openness and semi-openness are given. Moreover, pre-$ \omega _{s} $ -openness which is a strong form of $ \omega _{s} $-openness and independent of each of openness and pre-semi-openness is introduced. Furthermore, slight $ \omega _{s} $-continuity as a new class of functions which lies between slight continuity and slight semi-continuity is introduced. Several results related to slight $ \omega _{s} $-continuity are introduced, in particular, sufficient conditions for the equivalence between slight $ \omega _{s} $ -continuity and slight continuity, and between slight $ \omega _{s} $ -continuity and slight semi-continuity are given. In addition to these, $ \omega _{s} $-compactness as a new class of topological spaces that lies strictly between compactness and semi-compactness is introduced. It is proved that locally countable compact topological spaces are $ \omega _{s} $ -compact. Also, it is proved that anti-locally countable $ \omega _{s} $ -compact topological spaces are semi-compact. Several implications, examples, counter-examples, characterizations, and mapping theorems are introduced related to the above concepts are introduced.</p></abstract>

scholarly journals Topological spaces compact with respect to a set of filters

2014 ◽  
Vol 12 (7) ◽  
Author(s):  
Paolo Lipparini
Keyword(s):  
Topological Space ◽  
Limit Point ◽  
Topological Spaces ◽  
Sequential Compactness ◽  
Countable Compactness

AbstractIf is a family of filters over some set I, a topological space X is sequencewise -compact if for every I-indexed sequence of elements of X there is such that the sequence has an F-limit point. Countable compactness, sequential compactness, initial κ-compactness, [λ; µ]-compactness, the Menger and Rothberger properties can all be expressed in terms of sequencewise -compactness for appropriate choices of . We show that sequencewise -compactness is preserved under taking products if and only if there is a filter such that sequencewise -compactness is equivalent to F-compactness. If this is the case, and there exists a sequencewise -compact T 1 topological space with more than one point, then F is necessarily an ultrafilter. The particular case of sequential compactness is analyzed in detail.

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.

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