Theorems · Theorem · general topology
isProperMap_snd_of_compactSpace
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [CompactSpace X],
IsProperMap Prod.sndIf X is a compact topological space, then Prod.snd : X × Y → Y is a proper map.
- Defined in
- Mathlib.Topology.Maps.Proper.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 90 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
- CompactSpacestatement and proof · cited by 593
- IsProperMapstatement · cited by 66
- IsProperMap.compproof · cited by 15
- IsProperMap.prodMapproof · cited by 7
- Homeomorph.isProperMapproof · cited by 6
- isProperMap_idproof · cited by 5
- Homeomorph.punitProdproof · cited by 2
- isProperMap_constproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsClosed.vadd_left_of_isCompactproof · cited by 5
- IsClosed.smul_left_of_isCompactproof · cited by 5
- isClosedMap_snd_of_compactSpaceproof · cited by 1