Theorems · Theorem · general topology
IsOpenQuotientMap.weaklyLocallyCompactSpace
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [WeaklyLocallyCompactSpace X]
{f : X → Y}, IsOpenQuotientMap f → WeaklyLocallyCompactSpace Y- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.imageproof · cited by 5,609
- nhdsproof · cited by 5,554
- IsCompactproof · cited by 1,282
- Function.Surjective.forallproof · cited by 214
- IsCompact.imageproof · cited by 105
- IsOpenQuotientMapstatement and proof · cited by 65
- WeaklyLocallyCompactSpacestatement and proof · cited by 35
- WeaklyLocallyCompactSpace.exists_compact_mem_nhdsproof · cited by 28
- IsOpenQuotientMap.isOpenMapproof · cited by 16
- IsOpenQuotientMap.surjectiveproof · cited by 16
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