International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 433-442

Paracompactness with respect to an ideal

T. R. Hamlett,1 David Rose,2 and Dragan Janković3

1Department of Mathematics, East Central University, Ada 74820, Oklahoma, USA
2Southeastern College of the Assemblies of God, 1000 Longfellow Blvd., Lakeland 35801, Florida, USA
3Dept. of Mathematical Sciences, Cameron University, Lawton 73505, Oklahoma, USA

Received 26 May 1995; Revised 26 October 1995

Copyright © 1997 T. R. Hamlett et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An ideal on a set X is a nonempty collection of subsets of X closed under the operations of subset and finite union. Given a topological space X and an ideal of subsets of X, X is defined to be -paracompact if every open cover of the space admits a locally finite open refinement which is a cover for all of X except for a set in . Basic results are investigated, particularly with regard to the - paracompactness of two associated topologies generated by sets of the form UI where U is open and I and {U|U is open and UA, for some open set A}. Preservation of -paracompactness by functions, subsets, and products is investigated. Important special cases of -paracompact spaces are the usual paracompact spaces and the almost paracompact spaces of Singal and Arya [“On m-paracompact spaces”, Math. Ann., 181 (1969), 119-133].