International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 239-247
On strict and simple type extensions
Department of Mathematics, Southeast Missouri State University, Cape Girardeau 63701, Missouri, USA
Received 14 August 1996; Revised 21 November 1996
Copyright © 1998 Mohan Tikoo. 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.
Let be an extension of a space , let . For , let . In 1964, Banaschweski introduced the strict extension , and
the simple extension of (induced by ) having base and
, respectively. The extensions and have been extensively used since
then. In this paper, the open filters
for some , and is an open ultrafilter on
are used to define some new topologies on . Some of these topologies produce nice
extensions of . We study some interrelationships of these extensions with , and respectively.