Mathlib Map

Theorems · Definition · general topology

stoneCechUnit

{α : Type u} → [inst : TopologicalSpace α] → α → StoneCech α

The natural map from α to its Stone-Čech compactification.

Defined in
Mathlib.Topology.Compactification.StoneCech
Cited by
15 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
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Around this declaration

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

isInducing_stoneCechUnit · cited by 4isInducing_stoneCechUnitstoneCechExtend_extends · cited by 4stoneCechExtend_extendsdenseRange_stoneCechUnit · cited by 3denseRange_stoneCechUnitinjective_stoneCechUnit_of_t35Space · cited by 2injective_stoneCechUnit_o…CompletelyRegularSpace.exists_uniformSpace · cited by 1CompletelyRegularSpace.ex…continuous_stoneCechUnit · cited by 1continuous_stoneCechUnitisEmbedding_stoneCechUnit · cited by 1isEmbedding_stoneCechUniteq_if_stoneCechUnit_eq · cited by 1eq_if_stoneCechUnit_eqstoneCechExtend_stoneCechUnit · cited by 1stoneCechExtend_stoneCech…isDenseInducing_stoneCechUnit · cited by 1isDenseInducing_stoneCech…completelyRegularSpace_iff_isInducing_stoneCechUnit · cited by 0completelyRegularSpace_if…t35Space_iff_isEmbedding_stoneCechUnit · cited by 0t35Space_iff_isEmbedding_…StoneCech.projective · cited by 0StoneCech.projectivestoneCechEquivalence · cited by 0stoneCechEquivalenceisDenseEmbedding_stoneCechUnit · cited by 0isDenseEmbedding_stoneCec…TopologicalSpace · cited by 24529TopologicalSpaceStoneCech · cited by 16StoneCechT2Quotient.mk · cited by 8T2Quotient.mkpreStoneCechUnit · cited by 7preStoneCechUnitstoneCechUnitCITED BYCITES

Cites4

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Cited by16

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