IJPAM: Volume 105, No. 4 (2015)

COMPACTNESS OF P-CLOSED SPACES VIA
KATĚTOV'S METHOD AND ADHERENCE DOMINATORS

Terrence A. Edwards$^1$, James E. Joseph$^2$,
Myung H. Kwack$^3$, Bhamini M.P. Nayar$^4$
$^1$Department of Mathematics
University of the District of Columbia
Washington, DC. 20008, USA
$^{2,3}$Emeritus, Department of Mathematics
Howard University
Washington, DC 20059, USA
$^2$35 E Street NW #709
Washington, DC 20001, USA
$^3$782 Tiffany Pl.
Concord, CA 94518, USA
$^4$Department of Mathematics
Morgan State University
Baltimore, MD 21251, USA


Abstract. An adherence dominator on a topological space $X$ is a function $\pi$ from the collection of filter bases on $X$ to the family of closed subsets of $X$ satisfying $\mathcal A(\Omega) \subset \pi(\Omega)$ where $\mathcal A(\Omega)$ is the adherence of $\Omega$ [10] and $\pi\Omega=\bigcap_\Omega\pi F=\bigcap_{ \mathcal O}\pi V$, where $\mathcal O$ represents the open members of $\Omega$ . The notations $\pi\Omega$ and $ \mathcal A\Omega$ are used for the values of the functions $\pi$ and $\mathcal A$. The $\pi$-adherence may be adherence $\mathcal A$, $\theta$-adherence [16], $u$-adherence [4], [5], [8], $s$-adherence [7], [9], $f$-adherence [6], $\delta$-adherence [14], etc., of a filter base. The theorems in [2], [3] and [12] on Hausdorff-closed, Urysohn-closed, and regular-closed spaces are subsumed in this paper as well as compactness of other p-closed spaces, using Katětov’s method and adherence dominators.

Received: October 10, 2015

AMS Subject Classification: 54D25, 54A05, 54A20

Key Words and Phrases: filters, adherence dominator, compact, p-closed, Katětov

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DOI: 10.12732/ijpam.v105i4.19 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 4
Pages: 805 - 809


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