The main aim of this work is to make a comprehensive study of a weaker version of normality called ¿-normality. We give a survey study of ¿-closed, ¿-open, pre-closed and pre-open sets, which are the keys of both ¿-normality and ¿-pre-normality. Some properties of these sets are given and proved. ¿ -Normality is both a topological and an additive property, but neither a productive nor a hereditary property in general. The notion of ¿-generalized closed sets is used to obtain various characterizations and preservation theorems of ¿-normality. Some properties of almost regular as well as almost completely regular spaces are presented, and a few results of them are improved. Some relationships between ¿-normality and both almost regularity and almost complete regularity are given. The important results are about presenting some counterexamples; the first one is about a semi-normal Hausdorff space but not ¿-normal. The second one is about an almost normal Tychonoff space but not quasi-normal and the third one is about an almost normal Tychonoff space but not ¿-normal. Some other results are presented in this work.
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Dr. SADEQ ALI SAAD THABIT.Studied pure mathematics, topology at Universiti Sains Malaysia. Assistant professor at Hadhramout University, Almahra, Yemen.
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Taschenbuch. Zustand: Neu. Pi-normality in Topological Spaces and its Generalization | Basics, Concepts, Properties, Examples and some Results | Sadeq Ali Saad Thabit | Taschenbuch | Englisch | 2017 | Scholars' Press | EAN 9783330651388 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu. Artikel-Nr. 113166741
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