Theorems · Theorem · general topology
isHomeomorph_iff_exists_inverse
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
IsHomeomorph f ↔ Continuous f ∧ ∃ g, Function.LeftInverse g f ∧ Function.RightInverse g f ∧ Continuous gA map is a homeomorphism iff it is continuous and has a continuous inverse.
- Defined in
- Mathlib.Topology.Homeomorph.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement and proof · cited by 2,592
- Homeomorphproof · cited by 725
- Homeomorph.symmproof · cited by 365
- Homeomorph.toEquivproof · cited by 77
- IsHomeomorphstatement and proof · cited by 69
- Equiv.right_invproof · cited by 68
- Equiv.left_invproof · cited by 59
- Homeomorph.isHomeomorphproof · cited by 19
- IsHomeomorph.homeomorphproof · cited by 18
- IsHomeomorph.continuousproof · cited by 8
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