Separation axioms

topological space in which distinct points have disjoint neighbourhoods

axioms in topology defining notions of "separation"

lemma that a topological space is normal iff any 2 disjoint closed subsets can be separated by a continuous function

topological space in which every pair of disjoint closed sets has disjoint open neighborhoods

concept in topology

topological space in which a point and a closed set are, if disjoint, separable by neighborhoods

topological space in which every open cover has an open refinement that is locally finite

topological space in which all singleton sets are closed

topological space in which a point and a closed set are separable by a real-valued continuous function

type of relation for subsets of a topological space

topological relational characteristic

topological space where any two distinct points are separated by a continuous function

concept in algebraic topology

topological space whose topology is fully captured by its lattice of open sets