Theorems · Theorem · general topology
TopologicalSpace.NonemptyCompacts.isClosed_inter_nonempty_of_isClosed
∀ {α : Type u_1} [inst : TopologicalSpace α] {F : Set α}, IsClosed F → IsClosed {K | (↑K ∩ F).Nonempty}- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites10
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
- SetLike.coestatement · cited by 8,199
- Set.ofPredstatement · cited by 6,101
- Set.Nonemptystatement · cited by 2,627
- IsClosedstatement and proof · cited by 1,639
- IsClosed.preimageproof · cited by 138
- TopologicalSpace.NonemptyCompactsstatement · cited by 137
- TopologicalSpace.NonemptyCompacts.continuous_coeproof · cited by 5
- TopologicalSpace.vietoris.isClosed_inter_nonempty_of_isClosedproof · cited by 2
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