International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 37-42
doi:10.1155/S0161171297000069

Some results on [n,m]-paracompact and [n,m]-compact spaces

Hasan Z. Hdeib1 and Yusuf Ünlü2

1Department of Mathematics, Faculty of Science, Jordan University, Amman, Jordan
2Cukurova Univesitesi, Matematik Bolumu, Adana PK. 171, Turkey

Received 9 February 1988; Revised 20 March 1996

Copyright © 1997 Hasan Z. Hdeib and Yusuf Ünlü. 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.

Abstract

Let n and m be infinite cardinals with n≤m and n be a regular cardinal. We prove certain implications of [n,m]-strongly paracompact, [n,m]-paracompact and [n,m]-metacompact spaces. Let X be [n,∞]-compact and Y be a [n,m]-paracompact (resp. [n,∞]-paracompact), Pn-space (resp. wPn-space). If m=∑k<nmk we prove that X×Y is [n,m]-paracompact (resp. [n,∞]-paracompact