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Theorems · Theorem · general topology

Topology.IsClosedEmbedding.noncompactSpace

∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [NoncompactSpace X] {f : X → Y},
  Topology.IsClosedEmbedding f → NoncompactSpace Y
Defined in
Mathlib.Topology.Compactness.Compact
Cited by
1 results in Mathlib
Foundations
Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceNoncompactSpace
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Around this declaration

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NormedSpace.noncompactSpace · cited by 0NormedSpace.noncompactSpa…TopologicalSpace · cited by 24529TopologicalSpaceTopology.IsClosedEmbedding · cited by 195Topology.IsClosedEmbeddingNoncompactSpace · cited by 21NoncompactSpaceTopology.IsClosedEmbedding.tendsto_cocompact · cited by 9IsClosedEmbedding.tendsto…Filter.Tendsto.neBot · cited by 8Tendsto.neBotnoncompactSpace_of_neBot · cited by 2noncompactSpace_of_neBotIsClosedEmbedding.noncompactS…CITED BYCITES

Cites6

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Cited by1

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