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Theorems · Theorem · general topology

CompletelyNormalSpace.of_forall_isOpen_normalSpace

∀ {X : Type u_1} [inst : TopologicalSpace X], (∀ (s : Set X), IsOpen s → NormalSpace ↑s) → CompletelyNormalSpace X

Alias of the reverse direction of completelyNormalSpace_iff_forall_isOpen_normalSpace. A space is completely normal iff all open subspaces are normal.

Defined in
Mathlib.Topology.Separation.Regular
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0 results in Mathlib
Foundations
Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
Mathlib docsSourceLoogleLeanSearch

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Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Elem · cited by 7166Set.ElemIsOpen · cited by 2400IsOpenNormalSpace · cited by 84NormalSpaceCompletelyNormalSpace · cited by 9CompletelyNormalSpacecompletelyNormalSpace_iff_forall_isOpen_normalSpace · cited by 3completelyNormalSpace_iff…CompletelyNormalSpace.of_fora…CITED BYCITES

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