All Questions

A simple question. Let $ f:X\to Y $ be a function and let $ E_f:=\{(x, y): f (x)=f (y)\}\subset X\times X $. What is the name of the set $ E(f) $? It would be nice to have some reference also. It ...

Suppose that a topological space $X$ satisfies the following property (P): "Each uncountable disjoint open family is locally countable", where a family $\mathcal U$ of subsets of $X$ is ...