Atsuji has internally characterized those metric spaces X for which each real-valued continuous function on X is uniformly continuous as follows: (1) the set X' of limit points of X is compact, and (2 ...

A completely regular topological space 𝑋 is called a 𝑃-space if every zero-set in 𝑋 is open. An intermediate ring is a ring 𝐴(𝑋) of real-valued continuous functions on 𝑋 containing all the ...