Nagata-Smirnov revisited
by
Lew Ludwig
Denison University
Coauthors: Chuan Liu

Nagata-Smirnov characterized a topological space as metrizable if and only if it is regular and has a s-locally finite base. Burke, Engelking, and Lutzer showed it was enough to have just a s-hereditarily closure preserving base and indicated there exists a non-metrizable space that has a s-weakly hereditarily closure preserving (s-wHCP) base. In this paper, we discuss the properties of spaces with a s-weakly hereditarily closure preserving base and give some sufficient and necessary conditions for spaces with s-wHCP bases to be metrizable.

Date received: February 28, 2005