Monotone bases and separation properties
by
Robert W Heath
University Of Pittsburgh

ABSTRACT: Monotone base and separation properties R.W. Heath, University of Pittsburgh, Pittsburgh, PA15260. A weak monotone orthobase B for a space X is a base such that, for any infinite, monotone subcollection D of B, either the intersection of the members of D is open, or D is a basis for any point p in the intersection. The existance of such a base is a necessary and sufficient condition for a developable space to be semi-metrizable. Examples show that the class of spaces with such bases is properly contained in the intersection of the class of spaces with bases of countable order and the class of spaces with orthobases. Related separation properties are considered and some questions are posed.

Date received: February 16, 1998