Category:Topology Definitions

A

• Adjunction
• Adjunction (topology)

B

• Basis
• Basis criterion (topology)
• Basis for a topology
• Boundary (topology)
• Bounded
• Bounded (linear map)
• Bounded (sequence)
• Bounded (set)
• Bounded linear map
• Bounded sequence
• Bounded set
• Box topology

C

• C(I,X)
• C(X,Y)
• Canonical injection of the subspace topology
• Canonical projection of the product topology
• Canonical projections of the product topology
• Cauchy sequence
• Cauchy sequence/Definition
• Cauchy sequence/Short definition
• Characteristic property of the disjoint union topology
• Characteristic property of the disjoint union topology/Statement
• Characteristic property of the product topology/Statement
• Characteristic property of the subspace topology
• Characteristic property of the subspace topology/Statement
• Circle
• Closed interval
• Closed map
• Closed n-cell
• Closed set
• Closed sets
• Closure (set, topology)
• Closure (topology)
• Closure of a set in a topological space
• Closure, interior and boundary
• Coarser topology
• Compact
• Compact (topology)
• Compactness
• Complete metric space
• Completeness
• Concatenation of loops and paths (homotopy)
• Concatenation of paths and loops (homotopy)
• Cone
• Cone (topology)
• Connected (topology)
• Connected subset (topology)
• Connected topological space
• Constant loop
• Constant loop based at
• Constant loop based at a point
• Continuity
• Continuous
• Continuous function
• Continuous map
• Continuous maps
• Contractible topological space
• Convergence (sequence)
• Convergence of a sequence
• Convergent sequence
• Converges (sequence)
• Coproduct
• Coproduct (topology)
• Cover
• Covering

C cont.

• Covering map (topology)
• Covering map (topology)/Definition
• Covering space
• Covering space (topology)
• CW-complex

D

• Deformation retract
• Deformation retraction
• Deformation retraction/Definition
• Dense
• Dense set
• Differentiation
• Disconnected (topology)
• Disconnected (topology)/Definition
• Disconnected subset (topology)
• Disconnected topological space
• Discrete metric
• Discrete metric and topology
• Discrete metric and topology/Metric space definition
• Discrete metric and topology/Summary
• Discrete topology
• Disjoint union
• Disjoint union (topology)
• Disjoint union space (topology)
• Disjoint union topological space
• Disjoint union topology

E

• End point preserving homotopic
• End-point-preseriving homotopic
• End-point-preserving homotopic paths
• Equivalence of Cauchy sequences
• Equivalence of Cauchy sequences/Definition
• Euclidean distance
• Euclidean metric
• Even covering (topology)
• Evenly covered (topology)
• Evenly covered by a continuous map
• Evenly covers (topology)

F

• Finer topology
• Finite complement topology
• First homotopy group
• Fundamental group homomorphism induced by a continuous map
• Fundamental groups

G

• Geometrically independent set
• Graph
• Graph (topological manifold)

H

• Hausdorff
• Hausdorff space
• Homeomorphic
• Homeomorphic topological spaces have isomorphic fundamental groups
• Homeomorphism
• Homeomorphism (topology)
• Homomorphism
• Homomorphism (topology)
• Homotopic
• Homotopic maps
• Homotopic paths
• Homotopy
• Homotopy class
• Homotopy concatenation
• Homotopy equivalence
• Homotopy equivalent topological space
• Homotopy equivalent topological spaces
• HomotopyPage

I

• Image of a compact set is compact
• Indiscrete topology
• Inner-product space
• Interior
• Interior (topology)

I cont.

• Interior point (topology)

L

• Larger topology
• Lebesgue number
• Lifting of a continuous map through a covering map
• Limit (sequence)
• Limit point
• Line
• Lingering sequence
• List of topological properties
• Local homeomorphism
• Locally euclidean
• Locally euclidean of dimension n
• Locally Euclidean of dimension n
• Locally euclidean topological space
• Locally Euclidean topological space
• Locally Euclidean topological space of dimension n
• Locally homeomorphic
• Locally path connected (topology)
• Locally path connected topological space
• Locally path-connected (topology)
• Locally path-connected topological space
• Loop
• Loop (topology)
• Loop concatenation
• Loops

M

• Metric
• Metric induced by a norm
• Metric space
• Metric spaces
• Metric subspace
• Metric topology
• Metrically bounded set
• Metrics

N

• N-cell
• Natural projection
• Neighbourhood
• Neighbourhoods
• Norm
• Normal
• Normal topological space
• Normal topological space/Definition
• Normed spaces
• Nth homotopy group
• Null sequence

O

• Omega(X,b)
• Open and closed maps
• Open ball
• Open balls
• Open cover
• Open covering
• Open map
• Open n-cell
• Open neighbourhood
• Open neighbourhoods
• Open set
• Open sets
• Orientable surface

P

• Passing to the quotient
• Path
• Path (topology)
• Path concatenation (topology)
• Path connected (topology)
• Path connected topological space
• Path-connected (topology)
• Path-connected topological space
• Paths and loops in a topological space