Theorems · Theorem · general topology
IsHomeomorph.continuous
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
IsHomeomorph f → Continuous f- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement · cited by 2,592
- IsHomeomorphstatement and proof · cited by 69
Cited by9
Results whose statement or proof uses this declaration.
- IsHomeomorph.homeomorphproof · cited by 18
- IsHomeomorph.isStrictMapproof · cited by 2
- IsHomeomorph.compproof · cited by 1
- Equiv.isHomeomorph_iffproof · cited by 1
- isHomeomorph_iff_continuous_isClosedMap_bijectiveproof · cited by 1
- IsHomeomorph.isProperMapproof · cited by 1
- IsHomeomorph.prodMapproof · cited by 0
- IsHomeomorph.sumMapproof · cited by 0
- isHomeomorph_iff_exists_inverseproof · cited by 0