Given any two distinct points , there exist neighborhoods and of and , respectively, with . It then follows that finite subsets are closed.
T_2-Separation Axiom
See also
Separation Axioms, Set Closure, T2-SpaceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "T_2-Separation Axiom." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/T2-SeparationAxiom.html