List of general topology topics

This is a list of general topology topics. Topological space Topological property Open set, closed set Clopen set Closure (topology) Boundary (topology) Dense (topology) G-delta set, F-sigma set closeness (mathematics) neighbourhood (mathematics) Continuity (topology) Homeomorphism Local homeomorphism Open and closed maps Germ (mathematics) Base (topology), subbase Open cover Covering space Atlas (topology) Limit point Net (topology) Filter (topology) Ultrafilter Nowhere dense Baire space Banach–Mazur game Meagre set Comeagre set Compact space Relatively compact subspace Heine–Borel theorem Tychonoff's theorem Finite intersection property Compactification Measure of non-compactness Paracompact space Locally compact space Compactly generated space Axiom of countability Sequential space First-countable space Second-countable space Separable space Lindelöf space Sigma-compact space Connected space T0 space T1 space Hausdorff space Completely Hausdorff space Regular space Tychonoff space Normal space Urysohn's lemma Tietze extension theorem Paracompact Separated sets Direct sum and the dual construction product Subspace and the dual construction quotient Topological tensor product List of examples in general topology Discrete space Locally constant function Trivial topology Cofinite topology Finer topology Product topology Restricted product Quotient space Unit interval Continuum (topology) Extended real number line Long line (topology) Sierpinski space Cantor set, Cantor space, Cantor cube Space-filling curve Topologist's sine curve Uniform norm Weak topology Strong topology Hilbert cube Lower limit topology Sorgenfrey plane Real tree Compact-open topology Zariski topology Kuratowski closure axioms Unicoherent Solenoid (mathematics) Uniform continuity Lipschitz continuity Uniform isomorphism Uniform property Uniformly connected space Metric topology Manhattan distance Ultrametric space P-adic numbers, p-adic analysis Open ball Bounded subset Pointwise convergence Metrization theorems Complete space Cauchy sequence