Theorems · Theorem · general topology
not_specializes_iff_exists_closed
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X}, ¬x ⤳ y ↔ ∃ S, IsClosed S ∧ x ∈ S ∧ y ∉ S- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 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
- IsClosedstatement and proof · cited by 1,639
- Specializesstatement · cited by 176
- specializes_iff_forall_closedproof · cited by 2
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