Theorems · Theorem · general topology
TopologicalSpace.Opens.mem_compl
∀ {α : Type u_2} [inst : TopologicalSpace α] {U : TopologicalSpace.Opens α} {x : α}, x ∈ Uᶜ ↔ ∃ V, Disjoint V U ∧ x ∈ V- Defined in
- Mathlib.Topology.Sets.Opens
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Compl.complstatement · cited by 2,925
- Disjointstatement and proof · cited by 2,201
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- compl_eq_sSup_disjointproof · cited by 1
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