Theorems · Definition · general topology

CompletelyNormalSpace.casesOn

{X : Type u} →
  [inst : TopologicalSpace X] →
    {motive : CompletelyNormalSpace X → Sort u_1} →
      (t : CompletelyNormalSpace X) →
        ((completely_normal :
              ∀ ⦃s t : Set X⦄, Disjoint (closure s) t → Disjoint s (closure t) → Disjoint (nhdsSet s) (nhdsSet t)) →
            motive ⋯) →
          motive t

Defined in: Mathlib.Topology.Separation.Regular
Cited by: 0 results in Mathlib
Foundations: Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace

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

Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Filterstatement · cited by 8,121
Disjointstatement and proof · cited by 2,201
closurestatement and proof · cited by 1,254
nhdsSetstatement and proof · cited by 267
CompletelyNormalSpacestatement and proof · cited by 9

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