A
function f between two uniform spaces X and Y is called a
uniform isomorphism if it satisfies the following properties • f is a
bijection • f is
uniformly continuous • the
inverse function f^{-1} is uniformly continuous In other words, a
uniform isomorphism is a
uniformly continuous bijection between
uniform spaces whose
inverse is also uniformly continuous. If a uniform isomorphism exists between two uniform spaces they are called '
or '.
Uniform embeddings A '''''' is an injective uniformly continuous map i : X \to Y between uniform spaces whose inverse i^{-1} : i(X) \to X is also uniformly continuous, where the image i(X) has the subspace uniformity inherited from Y. ==Examples==