General Topology

A₁ algebraic axiom of choice B₁ basic nhood Cauchy closed sets closed subset closure cluster point collection compact Hausdorff space compact spaces compact subset compact-open topology compactification completely regular continuous functions continuous map converges defined Definition denote dense discrete disjoint open sets elements embedded equivalent example Exercise filter finite refinement function f h₁ Hausdorff space hence homeomorphic homotopy intersection interval Lemma Lindelöf Lindelöf space linear locally compact locally connected locally finite map ƒ Math metric space metrization theorem nhood base nonempty normal spaces one-one open cover open set P₁ paracompact space pointwise product space Proof pseudometric quotient result retract Section separable sequence ẞX subbase subcover subspace Suppose T₁-space T₂ topological space topology induced totally bounded Tychonoff space U₁ ultrafilter uniform cover uniform space uniformly continuous Urysohn usual topology w₁ weak topology x₁