Theorems · Theorem · general topology
Topology.isQuotientMap_iff_isStrictMap_surjective
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Topology.IsQuotientMap f ↔ Topology.IsStrictMap f ∧ Function.Surjective fQuotient maps are precisely surjective strict maps.
- Defined in
- Mathlib.Topology.Maps.Strict.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
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
- Set.Elemproof · cited by 7,166
- Set.rangeproof · cited by 4,705
- Homeomorphproof · cited by 725
- Topology.IsQuotientMapstatement and proof · cited by 124
- Function.Surjective.range_eqproof · cited by 70
- Homeomorph.transproof · cited by 49
- Topology.IsStrictMapstatement and proof · cited by 45
- Homeomorph.setCongrproof · cited by 29
- Topology.IsQuotientMap.surjectiveproof · cited by 24
- Homeomorph.isQuotientMapproof · cited by 22
- Homeomorph.Set.univproof · cited by 16
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