On the Cardinality of Urysohn Spaces

Abstract

AbstractIn this paper some cardinal inequalities for Urysohn spaces are established. In particular the following two theorems are proved:(i)If where [A]θ denotes the θ-closed hull of A, i.e., the smallest θ-closed subset of X containing A;(ii), where aL(X, X) is the smallest cardinal number m such that for every open cover of X there is a subfamily for which