Bookcover of An extension of semi-open sets with applications on spaces, functions
Booktitle:

An extension of semi-open sets with applications on spaces, functions

Topological Space

LAP LAMBERT Academic Publishing (2012-03-29 )

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ISBN-13:

978-3-8484-9322-7

ISBN-10:
3848493225
EAN:
9783848493227
Book language:
English
Blurb/Shorttext:
The aim of this work is to introduce and study a new class of set as an extension of semi-open sets in topological spaces called the Sw-open set. We use this set to define new types of continuous functions and new types of topological spaces.It is proved that every Sw-open set is dense and both the families SwO(X) and SO(X) coincide whenever the space X is hyperconnected. The topological spaces (X, τ) and (X, τα) have the same family of Sw-open sets.The concept of Sw-compactness is introduced and we prove that a space X is Sw-compact if and only if for every somewhat preopen cover of a space X there is a finite subcover under the condition that X is strongly irresolvable.Separation axioms are defined and characterized and it is proved that the space X is Sw-T2 whenever each point of X possesses an Sw-regular subset which is an Sw-T2 subspace in X.
Publishing house:
LAP LAMBERT Academic Publishing
Website:
https://www.lap-publishing.com/
By (author) :
Layla Saaddullah, Alyas Barakat
Number of pages:
176
Published at:
2012-03-29
Stock:
Available
Category:
Mathematics
Price:
68.00 €
Keywords:
Topological Space, Spaces, Sw-open set, Sw-continuous, Sw-compactness., semi-open sets

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