{"product_id":"pi-normality-in-topological-spaces-and-its-generalization-basics-concepts-properties-examples-and-some-results-von-sadeq-ali-saad-thabit","title":"Pi-normality in Topological Spaces and its Generalization","description":"\u003cp\u003eThe 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.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783330651388\"\u003e\u003ch3\u003eBasics, Concepts, Properties, Examples and some Results\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783330651388","offer_id":39429489819741,"sku":"9783330651388","price":79.9,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/f0b0786c-7a10-4de7-a4fb-e28462e7c5a8.jpg?v=1757651008","url":"https:\/\/shop.autorenwelt.de\/products\/pi-normality-in-topological-spaces-and-its-generalization-basics-concepts-properties-examples-and-some-results-von-sadeq-ali-saad-thabit","provider":"Autorenwelt Shop","version":"1.0","type":"link"}