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Theorems · Theorem · general topology

IsClosed.frontier_subset

∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsClosed s → frontier s ⊆ s

Alias of the reverse direction of frontier_subset_iff_isClosed.

Defined in
Mathlib.Topology.Closure
Cited by
2 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.

threeAPFree_frontier · cited by 1threeAPFree_frontierintrinsicFrontier_subset · cited by 0intrinsicFrontier_subsetSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceIsClosed · cited by 1639IsClosedfrontier · cited by 214frontierfrontier_subset_iff_isClosed · cited by 2frontier_subset_iff_isClo…IsClosed.frontier_subsetCITED BYCITES

Cites5

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.