Category:Definitions/Topology
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This category contains definitions related to Topology.
Related results can be found in Category:Topology.
Topology is a geometry of transformations in which the only invariant is continuity.
Some sources suggest that it can indeed be described simply as the study of continuity.
As such, it is closely interwoven with the branch of analysis.
Subcategories
This category has the following 109 subcategories, out of 109 total.
A
- Definitions/Adherent Points (4 P)
B
- Definitions/Baire Category (8 P)
- Definitions/Baire Spaces (5 P)
C
- Definitions/Cells (Topology) (1 P)
- Definitions/Closed Balls (10 P)
- Definitions/Closed Sets (17 P)
- Definitions/Cobordisms (5 P)
- Definitions/Complex Manifolds (empty)
- Definitions/Covering Spaces (1 P)
D
- Definitions/Derived Sets (1 P)
- Definitions/Dimension Theory (1 P)
- Definitions/Discrete Sets (1 P)
E
- Definitions/Everywhere Dense (12 P)
F
- Definitions/Fiber Bundles (11 P)
G
H
I
- Definitions/Irreducible Spaces (13 P)
- Definitions/Isolated Points (9 P)
J
- Definitions/Jordan Arcs (3 P)
- Definitions/Jordan Curves (10 P)
K
- Definitions/Klein Bottle (1 P)
L
- Definitions/Local Bases (3 P)
- Definitions/Loops (Topology) (11 P)
M
N
- Definitions/Nowhere Dense (3 P)
- Definitions/Null Sets (4 P)
O
- Definitions/Oscillation (12 P)
P
- Definitions/Paths (Topology) (3 P)
- Definitions/Perfect Sets (4 P)
- Definitions/Projections (8 P)
- Definitions/Proper Mappings (3 P)
Q
R
S
- Definitions/Schemes (21 P)
- Definitions/Separable Spaces (3 P)
- Definitions/Set Boundaries (9 P)
- Definitions/Set Closures (12 P)
- Definitions/Set Exteriors (4 P)
- Definitions/Set Interiors (5 P)
- Definitions/Submanifolds (3 P)
T
- Definitions/Tangent Bundles (2 P)
- Definitions/Topological Bases (12 P)
U
Pages in category "Definitions/Topology"
The following 200 pages are in this category, out of 297 total.
(previous page) (next page)A
B
- Definition:Baire Category
- Definition:Baire Property
- Definition:Baire Space (Topology)
- Definition:Basic Open Set
- Definition:Basis (Topology)
- Definition:Borel Set
- Definition:Borel Sigma-Algebra
- Definition:Borel Sigma-Algebra/Borel Set
- Definition:Borel Sigma-Algebra/Topological Space
- Definition:Boundary (Topology)
C
- Definition:Cantor-Bendixson Derivative
- Definition:Cantor-Bendixson Rank
- Definition:Category of Open Sets
- Definition:Cell (Topology)
- Definition:Character of Point in Topological Space
- Definition:Character of Topological Space
- Definition:Clopen (Topology)
- Definition:Clopen Set
- Definition:Closed Invariant
- Definition:Closed Locally Finite Set of Subsets
- Definition:Closed Mapping
- Definition:Closed Point
- Definition:Closed Set
- Definition:Closed Set (Topology)
- Definition:Closure (Topology)
- Definition:Coarser Topology
- Definition:Coarser Topology/Strictly Coarser
- Definition:Cobordism
- Definition:Cobordism/Also denoted as
- Definition:Codimension
- Definition:Cohomology Group
- Definition:Cohomology Theory
- Definition:Combinatorial Topology
- Definition:Compact Space/Topology
- Definition:Compactification
- Definition:Comparable Topologies
- Definition:Completely Metrizable Topology
- Definition:Concatenation (Topology)
- Definition:Condensation Point
- Definition:Connected (Topology)/Set
- Definition:Connected Component (Topology)
- Definition:Connected Space
- Definition:Connected Sum
- Definition:Continuous Group Action
- Definition:Continuous Invariant
- Definition:Continuous Mapping (Topology)
- Definition:Continuum
- Definition:Convergent Filter
- Definition:Convergent Filter Basis
- Definition:Convergent Sequence/Topology
- Definition:Countability Axioms
- Definition:Countable Basis
- Definition:Critical Point (Topology)
D
- Definition:Decomposable Set
- Definition:Decomposition (Topology)
- Definition:Dense
- Definition:Dense-in-itself
- Definition:Density of Topological Space
- Definition:Derived Set
- User:Dfeuer/Topological Field
- Definition:Dimension (Topology)
- Definition:Dimension (Topology)/Locally Euclidean Space
- Definition:Dimension Theory
- Definition:Discrete Set
- Definition:Discrete Set of Subsets
E
- Definition:Embedding (Topology)
- Definition:Entropy of Open Cover
- Definition:Equidecomposable
- Definition:Equidecomposable Sets
- Definition:Equivalent Topological Bases
- Definition:Euler Characteristic
- Definition:Evaluation Mapping (Topology)
- Definition:Evenly Covered
- Definition:Everywhere Dense
- Definition:Expansion of Topology
- Definition:Exterior (Topology)
F
G
- Definition:G-Delta Set
- Definition:Generated Topology
- Definition:Generic Point of Topological Space
- Definition:Generic Point of Topological Space/Definition 1
- Definition:Generic Point of Topological Space/Definition 2
- Definition:Genus
- Definition:Geometria Situs
- Definition:Geometric Topology
- Definition:Graph Theory
- Definition:Group Action by Homeomorphisms
H
I
- Definition:Identification Mapping
- Definition:Identification Topology/Identification Mapping
- Definition:Image of Topological Space
- Definition:Induced Topology
- Definition:Injective Space
- Definition:Inner Limit
- Definition:Interior (Topology)
- Definition:Interior Point (Topology)
- Definition:Interior Point (Topology)/Definition 1
- Definition:Interior Point (Topology)/Definition 2
- Definition:Interior Point (Topology)/Definition 3
- Definition:Irreducible Space
- Definition:Irreducible Subset
- Definition:Irreducible Subset (Topology)
- Definition:Isolated Point
- Definition:Isolated Point (Topology)
K
L
- Definition:Lattice of Bounded Continuous Real-Valued Functions
- Definition:Lattice of Continuous Real-Valued Functions
- Definition:Lattice of Real-Valued Functions
- User:Leigh.Samphier/Topology/Sober Space need not be T1
- User:Leigh.Samphier/Topology/T1 and Sober Space need not be T2
- User:Leigh.Samphier/Topology/T1 Space need not be Sober
- Definition:Lie Group
- Definition:Limit of Sequence/Topological Space
- Definition:Limit of Topological Spaces
- Definition:Limit Point
- Definition:Limit Point/Topology
- Definition:Limit Point/Topology/Point
- Definition:Limit Point/Topology/Set
- Definition:Limit Topology
- Definition:Local Basis
- Definition:Local Coordinates
- Definition:Local Dimension of Topological Space
- Definition:Local Sub-Basis
- Definition:Local Trivialization
- Definition:Locally Compact Hausdorff Space
- Definition:Locally Compact Space
- Definition:Locally Finite Set of Subsets
- Definition:Loop (Topology)
- Definition:Lower Limit (Topological Space)
M
N
- Definition:Neighborhood (Topology)
- Definition:Neighborhood of Infinity (Topology)
- Definition:Neighborhood Space
- Definition:Neighborhood System
- Definition:Net (Set Theory)
- Definition:Noetherian Topological Space
- User:NOrbeck/Definition:Isotopy
- Definition:Normal Bundle
- Definition:Normal Space/Manifold
- Definition:Nowhere Dense
- Definition:Null Set
O
- Definition:Omega-Accumulation Point
- Definition:Open Discrete Set of Subsets
- Definition:Open Invariant
- Definition:Open Locally Finite Set of Subsets
- Definition:Open Mapping
- Definition:Open Point
- Definition:Open Region
- Definition:Open Set
- Definition:Open Set/Topology
- Definition:Open Sigma-Discrete Set of Subsets
- Definition:Open Sigma-Locally Finite Set of Subsets
- Definition:Open Subset in Strong Operator Topology
- Definition:Open Subset in Uniform Operator Topology
- Definition:Open Subset in Weak Operator Topology
- Definition:Outer Limit
P
- Definition:Particular Point
- Definition:Partition of Unity (Topology)
- Definition:Partition of Unity (Topology)/Subordinate
- Definition:Path (Topology)
- Definition:Path (Topology)/Composable Paths
- Definition:Perfect Set
- Definition:Point Finite
- Definition:Point of Set
- Definition:Pointed Topological Space
- Definition:Polish Space
- Definition:Projection (Mapping Theory)
- Definition:Projective Space
- Definition:Projective Space/Real Projective Space