Co-Compact Separation Axioms and Slight Co-Continuity

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 continu...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 12; no. 10; p. 1614
Main Authors Al Ghour, Samer, Moghrabi, Enas
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.10.2020
Subjects
Axioms
Coc-open
Continuity (mathematics)
normality
Regularity
T2 property
Topology
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym12101614