Theorems · Theorem · general topology
IsClosedMap.isStrictMap
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
IsClosedMap f → Continuous f → Topology.IsStrictMap fA closed continuous map is a strict map.
- Defined in
- Mathlib.Topology.Maps.Strict.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 2,592
- IsClosedMapstatement and proof · cited by 138
- Topology.IsStrictMapstatement · cited by 45
- Set.rangeFactorization_surjectiveproof · cited by 20
- Topology.isStrictMap_iff_isQuotientMap_rangeFactorizationproof · cited by 5
- IsClosedMap.subtype_mkproof · cited by 4
- Continuous.rangeFactorizationproof · cited by 3
- IsClosedMap.isQuotientMapproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsClosedMap.isStrictMapproof · cited by 0