Results about the Alexandroff duplicate space

Khulod Almontashery, Lutfi Kalantan


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.


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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P. S. Alexandroff and P. S. and Urysohn, Mémoire sur les espaces topologiques compacts, Verh. Akad. Wetensch. Amsterdam, 14 (1929).

S. AlZahrani and L. Kalantan, $C$-normal topological property, Filomat, to appear.

A. V. Arhangelskii and L. Ludwig, On $alpha$-normal and $beta$-normal spaces, Comment. Math. Univ. Carolinae. 42, no. 3 (2001), 507-519.

E. K. van Douwen, The integers and topology, in: K. Kunen, J. E. Vaughan (Eds.), Handbook of set-Theoretic Topology, North-Holland,Amsterdam, 1984, pp. 111-167.


R. Engelking, General Topology, Vol. 6, Berlin: Heldermann (Sigma series in pure mathematics), Poland, 1989.

R. Engelking, On the double circumference of Alexandroff, Bull. Acad. Pol. Sci. Ser. Astron. Math. Phys. 16, no 8 (1968), 629-634.

L. Kalantan, Results about $kappa$-normality, Topology and its Applications 125, no. 1 (2002), 47-62.


L. Kalantan and F. Allahabi, On almost normality, Demonstratio Mathematica XLI, no. 4 (2008), 961-968.

L. Kalantan, $pi$-normal topological spaces, Filomat 22, no. 1 (2008), 173-181.


S. Mrówka, On completely regular spaces, Fundamenta Mathematicae 41 (1954), 105-106.

P. Nyikos, Axioms, theorems, and problems related to the Jones lemma, General topology

Academic Press, New York-London, 1981.

K. A. Ross and A. H. Stone, Product of separable spaces, Amer. Math. Month. 71(1964), 398-403.


L. A. Steen and J. A. Seebach, Counterexamples in topology, Dover Publications, INC., New York, 1995.

A. H. Stone, Paracompactness and product spaces, Bull. Amer. Soc. 54 (1948), 977-982.


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