Paracompactness with respect to an ideal
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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1997-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171297000598 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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]. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |