Spread and local properties

Abstract

A technique for combining the spread of a space and several local properties is exploited to obtain decompositions of a space and cardinal function bounds on the size and weight. It is shown that a locally countable set is the union of ω 1 {\omega _1} discrete sets and that under M A ( ω 1 ) MA\left ( {{\omega _1}} \right ) the weight of a manifold is equal to its spread.