A metrizability condition for topological spaces

The purpose of this thesis is to show that a necessary and sufficient condition that a topological space S be metrizable is that S be a [sum][lowered c]-space; that is, that there exists a sequence G[lowered 1], G[lowered 2]... such that: (1) for each positive integer n, G[lowered n] is a collection of open sets covering S, (2) for each positive integer n, G[lowered n+1] is a subcollection of G[lowered n], and (3) if p and q are two points of S and R is an open set containing p, then there exists a positive integer n such that if g and h are elements of G[lowered n], g contains p, and h intersects g then (g + h) is a subset of R and q does not belong to (g + h).Mathematics, Department o