Results about the Alexandroff duplicate space

Khulod Almontashery, Lutfi Kalantan

Abstract

In this paper, we present some new results about the  Alexandroff Duplicate Space. We prove that if a space X has the property P, then its Alexandroff Duplicate space A(X) may not have P, where P is one of the following properties: extremally disconnected, weakly extremally disconnected, quasi-normal, pseudo compact. We prove that if X is $\alpha$-normal, epinormal, or has property $\omega D$, then so is A(X). We prove almost normality is preserved by A(X) under special conditions.

Keywords

Alexandroff duplicate; normal; almst normal; mildly normal; quasi-normal; pseudo compact; Property $\omega D$; $\alpha$-normal; epinormal.

Subject classification

54F65; 54D15; 54G20.

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References

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Universitat Politècnica de València

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