A map f: X → Y is continuous iff f⁻¹(U) is open in X for every open U ⊆ Y. Generalises the ε-δ definition from analysis.
Continuous map
Related concepts
- Open set
- Homeomorphism
- Fundamental group π₁(X, x₀)
- Homotopy
- Homology H_n(X)
- Brouwer fixed-point theorem
- Morphism (arrow) f: A → B
- Smooth manifold
- Urysohn's lemma
- Covering space
- Fiber bundle
- Borsuk-Ulam theorem
- Hairy ball theorem
- Jordan curve theorem
- Tietze extension theorem
- Banach fixed-point theorem
- Invariance of domain