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.

Full Text:

PDF

References

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.

(http://dx.doi.org/10.1016/B978-0-444-86580-9.50006-9)

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.

(http://dx.doi.org/10.1016/S0166-8641(01)00258-9)

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.

(http://dx.doi.org/10.2298/FIL0801173K)

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.

(http://dx.doi.org/10.2307/2313241)

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.

(http://dx.doi.org/10.1090/S0002-9904-1948-09118-2)

Abstract Views

2268
Metrics Loading ...

Metrics powered by PLOS ALM


 

Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. Disconnection in the Alexandroff duplicate
Papiya Bhattacharjee, Michelle L. Knox, Warren Wm. McGovern
Applied General Topology  vol: 22  issue: 2  first page: 331  year: 2021  
doi: 10.4995/agt.2021.14602



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt