An -space is a topological space in which the topology is generated by the family of all -sets (see [N]). In this paper, minimal--spaces (where denotes several separation axioms) are investigated. Some new characterizations of -spaces are also obtained.
Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have nonempty interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.
It is shown that every Polish space X with admits a compact subspace Y such that where and denote the topological and Hausdorff dimensions, respectively.