Anthony W. Hager, Approximation Theorems for Uniformly Continuous Functions, Transactions of the American Mathematical Society, Vol. 236 (Feb., 1978), pp. 263-273 ...

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 ...

Technical Terms Bernstein polynomials: Polynomial functions that serve as building blocks for approximating continuous functions on closed intervals.