Quotient maps on spaces with point-countable bases
by
Alexander Shibakov
Auburn University, AL

We prove the following analog of a well known theorem of Lasnev:

Theorem 1. A closed map on a space with a point-countable base is perfect (i. e. has compact fibers) modulo a union of \omega₁ many relatively discrete subsets of the image.

Corollary 1.1. An image of a space with a point-countable base under a closed map is a union of \omega₁ spaces with point-countable bases.

The methods used in the proofs of these results are used to prove the following metrizability criterion for topological groups:

Theorem 2. A Hausdorff sequential topological group is metrizable if and only if it is an image of a metrizable space under a quotient map with separable fibers and has sequential order less than \omega₁.

Some examples and applications of these results are also given.

Date received: February 28, 1997

Copyright © 1997 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 # caam-37.