Urysohn's Lemma

Urysohn's Lemma is a fundamental result in topology stating that in a certain type of space called a normal topological space, if you have two distinct, non-overlapping "closed" sets, then it's possible to find a continuous function that maps the entire space to the interval [0, 1], such that one set maps to 0 and the other to 1. Essentially, it allows us to smoothly separate two separate closed sets with a function, demonstrating that the space has good separation properties and enabling constructions like "cutting" the space into parts via continuous transitions.