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This is a
list of
general topology
topics
.
Basic concepts
[
edit
]
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)
Limits
[
edit
]
Limit point
Net (topology)
Filter (topology)
Ultrafilter
Topological properties
[
edit
]
Baire category theorem
Nowhere dense
Baire space
Banach–Mazur game
Meagre set
Comeagre set
Compactness and countability
[
edit
]
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
Connectedness
[
edit
]
Connected space
Separation axioms
[
edit
]
T0 space
T1 space
Hausdorff space
Completely Hausdorff space
Regular space
Tychonoff space
Normal space
Urysohn's lemma
Tietze extension theorem
Paracompact
Separated sets
Topological constructions
[
edit
]
Direct sum
and the dual construction
product
Subspace
and the dual construction
quotient
Topological tensor product
Examples
[
edit
]
See also:
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 spaces
[
edit
]
Uniform continuity
Lipschitz continuity
Uniform isomorphism
Uniform property
Uniformly connected space
Metric spaces
[
edit
]
Metric topology
Manhattan distance
Ultrametric space
P-adic numbers
,
p-adic analysis
Open ball
Bounded subset
Pointwise convergence
Metrization theorems
Complete space
Cauchy sequence
Banach fixed-point theorem
Polish space
Hausdorff distance
Intrinsic metric
Category of metric spaces
Topology and
order theory
[
edit
]
Stone duality
Stone's representation theorem for Boolean algebras
Specialization (pre)order
Sober space
Spectral space
Alexandrov topology
Upper topology
Scott topology
Scott continuity
Lawson topology
Descriptive set theory
[
edit
]
Polish Space
Cantor space
Dimension theory
[
edit
]
Main article:
Dimension
Inductive dimension
Lebesgue covering dimension
Lebesgue's number lemma
Combinatorial topology
[
edit
]
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
[
edit
]
Simply connected
Semi-locally simply connected
Path (topology)
Homotopy
Homotopy lifting property
Pointed space
Wedge sum
Smash product
Cone (topology)
Adjunction space
Topology and algebra
[
edit
]
Topological algebra
Topological group
Topological ring
Topological vector space
Topological module
Topological abelian group
Properly discontinuous
Sheaf space
See also
[
edit
]
Topology glossary
List of topology topics
List of geometric topology topics
List of algebraic topology topics
Publications in topology
v
t
e
Topology
Fields
General (point-set)
Algebraic
Combinatorial
Continuum
Differential
Geometric
low-dimensional
Homology
cohomology
Set-theoretic
Digital
Key concepts
Open set
/
Closed set
Interior
Continuity
Space
compact
connected
Hausdorff
metric
uniform
Homotopy
homotopy group
fundamental group
Simplicial complex
CW complex
Polyhedral complex
Manifold
Bundle (mathematics)
Second-countable space
Cobordism
Metrics and properties
Euler characteristic
Betti number
Winding number
Chern number
Orientability
Key results
Banach fixed-point theorem
De Rham cohomology
Invariance of domain
Poincaré conjecture
Tychonoff's theorem
Urysohn's lemma
Category
Mathematics portal
Wikibook
Wikiversity
Topics
general
algebraic
geometric
Publications
v
t
e
Wikipedia 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
R
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https://en.wikipedia.org/w/index.php?title=List_of_general_topology_topics&oldid=1182627983
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