 List of general topology topics

This is a list of general topology topics, by Wikipedia page.
Contents
Basic concepts
 Topological space
 Topological property
 Open set, closed set
 Clopen set
 Closure (topology)
 Boundary (topology)
 Dense (topology)
 Gdelta set, Fsigma set
 closeness (mathematics)
 neighbourhood (mathematics)
 Continuity (topology)
 Base (topology), subbase
 Open cover
 Covering space
 Atlas (topology)
Limits
 Limit point
 Net (topology)
 Filter (topology)
 Ultrafilter
Topological properties
 Baire category theorem
 Nowhere dense
 Baire space
 BanachMazur game
 Meagre set
 Comeagre set
Compactness and countability
 Compact space
 Paracompact space
 Locally compact space
 Compactly generated space
 Axiom of countability
 Sequential space
 Firstcountable space
 Secondcountable space
 Separable space
 Lindelöf space
 Sigmacompact space
Connectedness
Separation axioms
 T0 space
 T1 space
 Hausdorff space
 Regular space
 Tychonoff space
 Normal space
 Urysohn's lemma
 Tietze extension theorem
 Paracompact
 Separated sets
Topological constructions
 direct sum and the dual construction product
 subspace and the dual construction quotient
 Topological tensor product
Examples
See also: List of examples in general topology.
 Discrete space
 Trivial topology
 Cofinite topology
 Finer topology
 Product topology
 Quotient space
 Unit interval
 Continuum (topology)
 Extended real number line
 Long line (topology)
 Sierpinski space
 Cantor set, Cantor space, Cantor cube
 Spacefilling curve
 Topologist's sine curve
 Uniform norm
 Weak topology
 Strong topology
 Hilbert cube
 Lower limit topology
 Sorgenfrey plane
 Real tree
 Compactopen topology
 Zariski topology
 Kuratowski closure axioms
 Unicoherent
 Solenoid (mathematics)
Uniform spaces
 Uniform continuity
 Lipschitz continuity
 Uniform isomorphism
 Uniform property
 Uniformly connected space
Metric spaces
 Metric topology
 Manhattan distance
 Ultrametric space
 Padic numbers, padic analysis
 Open ball
 Bounded subset
 Pointwise convergence
 Metrization theorems
 Complete space
 Polish space
 Hausdorff distance
 Intrinsic metric
 Category of metric spaces
Topology and order theory
 Stone duality
 Specialization (pre)order
 Sober space
 Spectral space
 Alexandrov topology
 Upper topology
 Scott topology
 Lawson topology
Descriptive set theory
Dimension theory
See also main article dimension
Combinatorial topology
 Polytope
 Simplex
 Simplicial complex
 CW complex
 Manifold
 Triangulation
 Barycentric subdivision
 Sperner's lemma
 Simplicial approximation theorem
 Nerve of an open covering
Foundations of algebraic topology
 Simply connected
 Semilocally simply connected
 Path (topology)
 Homotopy
 Homotopy lifting property
 Pointed space
 Wedge sum
 smash product
 Cone (topology)
 Adjunction space
Topology and algebra
 Topological algebra
 Topological group
 Topological ring
 Topological vector space
 Topological module
 Topological abelian group
 Properly discontinuous
 Sheaf space
See also
 Topology glossary
 List of topology topics
 List of geometric topology topics
 List of algebraic topology topics
 Publications in topology
Outlines  General reference
 Culture and the arts
 Geography and places
 Health and fitness
 History and events
 Mathematics and logic
 Natural and physical sciences
 People and self
 Philosophy and thinking
 Religion and belief systems
 Society and social sciences
 Technology and applied sciences
Categories: Mathematicsrelated lists
 General topology
 Outlines
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