Mathlib Map

Theorems · Theorem · general topology

IsClosed.isClosedEmbedding_subtypeVal

∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsClosed s → Topology.IsClosedEmbedding Subtype.val
Defined in
Mathlib.Topology.Constructions
Cited by
19 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsClosed.isClosedMap_subtype_val · cited by 8IsClosed.isClosedMap_subt…IsClosed.polishSpace · cited by 6IsClosed.polishSpaceNNReal.isClosedEmbedding_coe · cited by 4NNReal.isClosedEmbedding_…IsClosed.tendsto_coe_cofinite_of_isDiscrete · cited by 4IsClosed.tendsto_coe_cofi…Matrix.SpecialLinearGroup.isClosedEmbedding_val · cited by 2SpecialLinearGroup.isClos…loc_compact_Haus_tot_disc_of_zero_dim · cited by 2loc_compact_Haus_tot_disc…BoundedContinuousFunction.exists_norm_eq_domRestrict_eq_of_closed · cited by 1BoundedContinuousFunction…Stonean.extremallyDisconnected_preimage · cited by 1Stonean.extremallyDisconn…IsClosed.isCompletelyPseudoMetrizableSpace · cited by 1IsClosed.isCompletelyPseu…IsClosed.isProperMap_subtypeVal · cited by 1IsClosed.isProperMap_subt…IsCompactOperator.codRestrict · cited by 1IsCompactOperator.codRest…BoundedContinuousFunction.exists_forall_mem_domRestrict_eq_of_closed · cited by 1BoundedContinuousFunction…IsClosed.weaklyLocallyCompactSpace · cited by 0IsClosed.weaklyLocallyCom…ArzelaAscoli.isCompact_closure_of_isClosedEmbedding · cited by 0ArzelaAscoli.isCompact_cl…isClosed_intrinsicClosure · cited by 0isClosed_intrinsicClosureSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceIsClosed · cited by 1639IsClosedTopology.IsClosedEmbedding · cited by 195Topology.IsClosedEmbeddingTopology.IsClosedEmbedding.subtypeVal · cited by 4IsClosedEmbedding.subtype…IsClosed.isClosedEmbedding_su…CITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by19

Results whose statement or proof uses this declaration.