Relationshipe between several properties of relative metacompactness type and paracompactness type
by
Elise M Grabner
Slippery Rock University, USA
Coauthors: Gary Grabner (Slippery Rock University, USA), Kazumi Miyazaki (Ehime University, Japan)

We present examples and results clarifying the relationship between some properties of relative metacompactness and paracompactness type.

Theorem 1 Suppose that X is a regular space. If a subset A of X is metacompact in X then A is weakly cp- metacompact in X.

Example 2 A Tychonoff space X and a subspace C of X which is 2- paracompact in X but which is not metacompact in X from outside.

Example 3 Spaces X and Y, perfect mapping f:X --> Y and a subset C of X which is 2- paracompact in X but f(C)=Y is not metacompact.

Date received: June 16, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeu-23.