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Theorems · Theorem · general topology

Topology.IsInducing.completelyRegularSpace

∀ {X : Type u} [inst : TopologicalSpace X] {Y : Type v} [inst_1 : TopologicalSpace Y] [CompletelyRegularSpace Y]
  {f : X → Y}, Topology.IsInducing f → CompletelyRegularSpace X
Defined in
Mathlib.Topology.Separation.CompletelyRegular
Cited by
2 results in Mathlib
Foundations
Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceCompletelyRegularSpace
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Around this declaration

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

completelyRegularSpace_iff_isInducing_stoneCechUnit · cited by 0completelyRegularSpace_if…completelyRegularSpace_induced · cited by 0completelyRegularSpace_in…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Elem · cited by 7166Set.ElemSet.preimage · cited by 4946Set.preimageContinuous · cited by 2592ContinuousIsClosed · cited by 1639IsClosedunitInterval · cited by 607unitIntervalSet.EqOn · cited by 603Set.EqOnContinuous.comp · cited by 371Continuous.compTopology.IsInducing · cited by 266Topology.IsInducingSet.mem_preimage · cited by 190Set.mem_preimageTopology.IsInducing.continuous · cited by 48IsInducing.continuousSet.mapsTo_preimage · cited by 35Set.mapsTo_preimageCompletelyRegularSpace · cited by 23CompletelyRegularSpaceTopology.IsInducing.isClosed_iff · cited by 8IsInducing.isClosed_iffIsInducing.completelyRegularS…CITED BYCITES

Cites17

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

Cited by2

Results whose statement or proof uses this declaration.