Separable topological space
= Separable topological space
= Topological separability
{synonym}
A <topological space> is separable when it has a countable <dense subset>. The topology is part of the assertion: a dual may be separable in its <weak-star topology> and not in its <norm topology>. A compact <metric space> is separable by taking the union of finite nets at scales tending to zero.