On Locally Compact Hausdorff Spaces with Finite Metrizability Number
by
M. Ismail
Dept. of Mathematics, Slippery Rock Univ., Slippery Rock, PA 16057
Coauthors: A. Szymanski

The metrizability number of a space X, denoted by m(X), is the smallest cardinal number k such that X can be represented as a union of k metrizable subspaces. In this paper, we consider locally compact Hausdorff spaces with finite metrizability number. We prove the following structure theorem and consider some of its consequences.

Theorem. If X is a locally compact Hausdorff space, m(X)=n, where n is finite and n > 1, then for each k, 0 < k < n, there exists an open dense subspace G of X such that m(G)=k and m(F)=n-k, where F=X-G.

Date received: June 3, 1999