Paracompactness with respect to an ideal

T. R. Hamlett, David Rose and Dragan Janković

International Journal of Mathematics and Mathematical Sciences, 1997, vol. 20, 1-10

Abstract:

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 ℐ of subsets of X , X is defined to be ℐ -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 ℐ . Basic results are investigated, particularly with regard to the ℐ - paracompactness of two associated topologies generated by sets of the form U − I where U is open and I ∈ ℐ and ⋃ { U | U is open and U − A ∈ ℐ , for some open set A }. Preservation of ℐ -paracompactness by functions, subsets, and products is investigated. Important special cases of ℐ -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].

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:973746

DOI: 10.1155/S0161171297000598

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