Theorems · Theorem · general topology

Topology.IsClosedEmbedding.sigmaCompactSpace

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [SigmaCompactSpace X]
  {e : Y → X}, Topology.IsClosedEmbedding e → SigmaCompactSpace Y

Defined in: Mathlib.Topology.Compactness.SigmaCompact
Cited by: 1 results in Mathlib
Foundations: Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace SigmaCompactSpace

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Cites12

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.preimageproof · cited by 4,946
Set.univproof · cited by 3,945
Topology.IsClosedEmbeddingstatement and proof · cited by 195
SigmaCompactSpacestatement and proof · cited by 55
Set.preimage_univproof · cited by 46
Set.preimage_iUnionproof · cited by 43
compactCoveringproof · cited by 14
Topology.IsClosedEmbedding.isCompact_preimageproof · cited by 12
isCompact_compactCoveringproof · cited by 8
iUnion_compactCoveringproof · cited by 5

Cited by1

Results whose statement or proof uses this declaration.

IsClosed.sigmaCompactSpaceproof · cited by 0