IJPAM: Volume 105, No. 4 (2015)
KATĚTOV'S METHOD AND ADHERENCE DOMINATORS


Myung H. Kwack



University of the District of Columbia
Washington, DC. 20008, USA

Howard University
Washington, DC 20059, USA

Washington, DC 20001, USA

Concord, CA 94518, USA

Morgan State University
Baltimore, MD 21251, USA
Abstract. An adherence dominator on a topological space is a function
from the collection of filter bases on
to the family of closed subsets of
satisfying
where
is the adherence of
[10]
and
, where
represents the open
members of
. The notations
and
are used for the values of the
functions
and
. The
-adherence may be adherence
,
-adherence [16],
-adherence [4], [5], [8],
-adherence [7], [9],
-adherence [6],
-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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This work is licensed under the Creative Commons Attribution International License (CC BY).