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

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