On Some Generalization of Paracompactness

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Abstract


The generalization of paracompact spaces via so-sets, sets are unions of open and nowhere dense sets, was studied. The aim of this paper is to establish the relationship between so-paracompact spaces and other generalizations of paracompact spaces and clarify the conditions under which the so-paracompact space is compact. The problem is solved by methods of general topology. It is proved that the sequentially compact so-paracompact space is compact. It is proved that the so-paracompactness saved when multiplied by the compact. Previously, other authors introduced the concept of S-paracompact space, based on the semi-open sets. Class of so-paracompact spaces wider than the class S-paracompact spaces. This paper shows that there are so-paracompact spaces which are not S-paracompact.

About the authors

V L Kljushin

Peoples’ Friendship University of Russia

Email: vklyushin@mail.ru
Higher Mathematics Department

- Jalal Hatem Hussein Al Bayati

Peoples’ Friendship University of Russia

Higher Mathematics Department

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Copyright (c) 2013 Клюшин В.Л., Джелал Хатем Хуссейн Аль Баяти -.

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