General topology Continuous maps Concept
Continuous map
Summary
A continuous map is a function that sends nearby points to nearby points. Between topological spaces, this means that preimages of open sets are open. Between metric spaces, it is the same as the epsilon-delta condition.
Where this leads
73 pages build on this one.
- Relative CW complex
- Topological dynamics
- Homotopy
- Chain recurrence
- Perfect map
- Milnor–Thurston kneading theory
- Michael selection theorem
- Homotopic maps
- Ringed space
- Analytic set
- Adjunction space
- Lefschetz number
- Invariance of domain
- Hurewicz fibration
- Absolute neighborhood retract
- Continuous multiplication
- Sheaf
- Homotopy equivalence
- Locally ringed space
- Symbolic dynamics
- Period three implies chaos
- Final topology
- Topological vector space
- Disjoint union topology
- Non-wandering set
- Semitopological group
- Gleason's theorem on projective compact spaces
- Hemicontinuity
- Topological transitivity
- Degree of a continuous map
- Recurrent point
- Regular function
- Cofibration
- Morphism of schemes
- Lefschetz fixed-point theorem
- Ham sandwich theorem
- Nielsen fixed-point theory
- Initial topology
- Compactly generated space
- Variational principle for topological entropy
- Minimal set
- Category of topological spaces
- Topological transformation group
- Topological entropy
- Wandering set
- Stone–Čech compactification
- Brouwer fixed-point theorem
- Topological mixing
- Sierpiński space
- Topological group
- Equicontinuous system
- Pointed space
- Borsuk–Ulam theorem
- Dugundji extension theorem
- Devaney chaos
- Weak homotopy equivalence
- Equivariant index theorem
- Proper map
- Compact-open topology
- Mapping cylinder
- G-signature theorem
- Necklace splitting theorem
- Morphism of varieties
- Pseudocompact space
- Borsuk's conjecture
- Continuous group homomorphism
- Geometric realization
- Morphism
- Covering space
- Sharkovskii's theorem
- Manifold with boundary
- Semicontinuity
- No-retraction theorem
Further reading
- Web https://en.wikipedia.org/wiki/Continuous_function, lead section
About this page
| Tag | 0VGFHTM75Y |
|---|---|
| URI | m2://0VGFHTM75Y |
| Aliases | continuous-function |
| Kind | concept |
| Writing | W0 stub |
| MSC | 54C05 |
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What links here
Special cases
Definitions
Used by
- Topological dynamics
- Homotopy
- Chain recurrence
- Perfect map
- Michael selection theorem
- Homotopic maps
- Ringed space
- Analytic set
- Adjunction space
- Lefschetz number
- Invariance of domain
- Hurewicz fibration
- Absolute neighborhood retract
- Continuous multiplication
- Sheaf
- Homotopy equivalence
- Locally ringed space
- Symbolic dynamics
- Period three implies chaos
- Final topology
- Topological vector space
- Disjoint union topology
- Non-wandering set
- Semitopological group
- Gleason's theorem on projective compact spaces
- Hemicontinuity
- Topological transitivity
- Degree of a continuous map
- Recurrent point
- Regular function
- Cofibration
- Morphism of schemes
- Lefschetz fixed-point theorem
- Nielsen fixed-point theory
- Initial topology
- Compactly generated space
- Variational principle for topological entropy
- Minimal set
- Category of topological spaces
- Topological transformation group
- Topological entropy
- Wandering set
- Stone–Čech compactification
- Brouwer fixed-point theorem
- Topological mixing
- Sierpiński space
- Topological group
- Equicontinuous system
- Pointed space
- Borsuk–Ulam theorem
- Dugundji extension theorem
- Devaney chaos
- Weak homotopy equivalence
- Proper map
- Compact-open topology
- Mapping cylinder
- Morphism of varieties
- Pseudocompact space
- Continuous group homomorphism
- Morphism
- Covering space
- Sharkovskii's theorem
- Semicontinuity
- No-retraction theorem