On θ-regular spaces
In this paper we study θ-regularity and its relations to other topological properties. We show that the concepts of θ-regularity (Janković, 1985) and point paracompactness (Boyte, 1973) coincide. Regular, strongly locally compact or paracompact spaces are θ-regular. We discuss the problem when a (co...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1994-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171294000979 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567609112920064 |
|---|---|
| author | Martin M. Kovár |
| author_facet | Martin M. Kovár |
| author_sort | Martin M. Kovár |
| collection | DOAJ |
| description | In this paper we study θ-regularity and its relations to other topological properties. We show that the concepts of θ-regularity (Janković, 1985) and point paracompactness (Boyte, 1973) coincide. Regular, strongly locally compact or paracompact spaces are θ-regular. We discuss the problem when a (countably) θ-regular space is regular, strongly locally compact, compact, or paracompact. We also study some basic properties of subspaces of a θ-regular space. Some applications: A space is paracompact iff the space is countably θ-regular and semiparacompact. A generalized Fσ-subspace of a paracompact space is paracompact iff the subspace is countably θ-regular. |
| format | Article |
| id | doaj-art-aff5484df543484ebf8b9736101c6e40 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-aff5484df543484ebf8b9736101c6e402025-02-03T01:01:08ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117468769210.1155/S0161171294000979On θ-regular spacesMartin M. Kovár0Department of Mathematics, Faculty of Electrical Engineering, Technical University of Brno, Areál VUT, Kraví Hora 21/XV, Brno 602 00, Czech RepublicIn this paper we study θ-regularity and its relations to other topological properties. We show that the concepts of θ-regularity (Janković, 1985) and point paracompactness (Boyte, 1973) coincide. Regular, strongly locally compact or paracompact spaces are θ-regular. We discuss the problem when a (countably) θ-regular space is regular, strongly locally compact, compact, or paracompact. We also study some basic properties of subspaces of a θ-regular space. Some applications: A space is paracompact iff the space is countably θ-regular and semiparacompact. A generalized Fσ-subspace of a paracompact space is paracompact iff the subspace is countably θ-regular.http://dx.doi.org/10.1155/S0161171294000979θ-regularitypoint paracompactnesscoversfilter basesnetsθ-closureθ-cluster point. |
| spellingShingle | Martin M. Kovár On θ-regular spaces International Journal of Mathematics and Mathematical Sciences θ-regularity point paracompactness covers filter bases nets θ-closure θ-cluster point. |
| title | On θ-regular spaces |
| title_full | On θ-regular spaces |
| title_fullStr | On θ-regular spaces |
| title_full_unstemmed | On θ-regular spaces |
| title_short | On θ-regular spaces |
| title_sort | on θ regular spaces |
| topic | θ-regularity point paracompactness covers filter bases nets θ-closure θ-cluster point. |
| url | http://dx.doi.org/10.1155/S0161171294000979 |
| work_keys_str_mv | AT martinmkovar onthregularspaces |