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 ...

It is shown that on every infinite-dimensional separable normed space there exist continuous real-valued functions that are nowhere locally uniformly continuous. An ...

Topological spaces form the foundational framework for modern analysis and geometry, characterised by a set equipped with a collection of open subsets satisfying specific axioms. This flexible ...