REMARKS AND QUESTIONS ON BASE POSITIONAL DIMENSION-LIKE FUNCTIONS OF THE TYPE IND

Abstract

Let Q be a subset of a space X. A family A of open subsets ofX is said to be a p-base for Q in X if the set {Q ∩ U : U ∈ A} is a base forthe subspace Q. In [12] base positional dimension-like functions of the typeind were introduced. The domain of these functions is the class of all p-bases.These functions were studied only with respect to the property of universality.Here, we study these functions with respect to other standard properties ofdimension theory and we present questions concerning these functions