More cardinal inequalities in T1/Urysohn spaces

Ramírez-Páramo, Alejandro; Cruz-Castillo, Ricardo

doi:10.1016/j.topol.2019.106847

Cited by 2 publications

(2 citation statements)

References 5 publications

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“…The work of Velicko was continued by many topologists. Recently; authors in [2,3,4,5,6,7] have obtained several interesting results related to these sets. The notions of -closed sets and -open sets are introduced by Hdeib [8].…”

Section: Introductionmentioning

confidence: 99%

A new class between theta open sets and theta omega open sets

Ghour

Al-Zoubi

2021

Heliyon

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We define  -closure operator as a new topological operator which lies between the -closure and the -closure. Some relationships between this new operator and each of -closure, -closure, and usual closure are obtained. Via  -closure operator, we introduce  -open sets as a new topology. Some mapping theorems related to the new topology are given. 2 topological spaces are characterized in terms of  -closure operator. Also, we use  -open sets to define  -regularity as a new separation axiom which lies strictly between -regularity and regularity. For a given topological space ( , ), we show that  -regularity is equivalent to the condition =  . Finally,  -continuity,  --continuity, weak  -continuity, and faint  -continuity are introduced and studied. Definition 2.1.[1] Let be a subset of a ts ( , ).a. The -closure of is denoted by ( ) and defined by

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Section: Introductionmentioning

confidence: 99%

A new class between theta open sets and theta omega open sets

Ghour

Al-Zoubi

2021

Heliyon

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“…Defining a new type of generalized open sets and utilizing it to define new topological concepts is now a very hot research topic [1][2][3][4][5][6][7][8][9][10][11]. As a new type of generalized open sets, Al-Ghour and Samarah in [12] defined coc-open sets as follows: A subset A of a topological space (X, τ) is called coc-open set if A is a union of sets of the form V − C, where V ∈ τ and C is a compact subset of X.…”

Section: Introductionmentioning

confidence: 99%

Co-Compact Separation Axioms and Slight Co-Continuity

Ghour

Moghrabi

2020

Symmetry

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Via co-compact open sets we introduce co-T2 as a new topological property. We show that this class of topological spaces strictly contains the class of Hausdorff topological spaces. Using compact sets, we characterize co-T2 which forms a symmetry. We show that co-T2 propoerty is preserved by continuous closed injective functions. We show that a closed subspace of a co-T2 topological space is co-T2. We introduce co-regularity as a weaker form of regularity, s-regularity as a stronger form of regularity and co-normality as a weaker form of normality. We obtain several characterizations, implications, and examples regarding co-regularity, s-regularity and co-normality. Moreover, we give several preservation theorems under slightly coc-continuous functions.

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More cardinal inequalities in T1/Urysohn spaces

Cited by 2 publications

References 5 publications

A new class between theta open sets and theta omega open sets

A new class between theta open sets and theta omega open sets

Co-Compact Separation Axioms and Slight Co-Continuity

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