A Note on Blumberg Pairs

Abstract

If X and Y are topological spaces, we say that (X, Y) is a Blumberg pair (“BP”) if it is true that for every f : X + Y, there exists a dense subset D of X such that $\left.\text{f}\right|\text{D}$ is continuous. w(X), d(X), and c(X) denote the weight, density character, and cellularity (or Souslin number) of X.