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Theorems · Theorem · general topology

IsClosed.not_specializes

∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X} {s : Set X}, IsClosed s → x ∈ s → y ∉ s → ¬x ⤳ y
Defined in
Mathlib.Topology.Inseparable
Cited by
2 results in Mathlib
Foundations
Depth 77 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.

OnePoint.not_specializes_infty_coe · cited by 2OnePoint.not_specializes_…AlgebraicGeometry.Scheme.height_of_isClosed · cited by 0Scheme.height_of_isClosedSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceIsClosed · cited by 1639IsClosedSpecializes · cited by 176SpecializesSpecializes.mem_closed · cited by 8Specializes.mem_closedIsClosed.not_specializesCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.