Definition for "Urysohn's Lemma" in the Quantum Dictionary

- Natural & Formal Sciences -

Mathematics & Logic Dictionary

In a normal topological space X, for any two disjoint closed sets A and B there exists a continuous function f: X → [0,1] such that f equals 0 on A and 1 on B; this constructs a continuous separator between closed sets.

- Mathematics & Logic -

Pure Mathematics Dictionary

In a normal topological space, any two disjoint closed sets can be separated by a continuous real-valued function: there exists a continuous map f : X → [0,1] with f = 0 on one closed set and f = 1 on the other.