Theorems · Theorem · general topology
frontier_eq_empty_iff
∀ {α : Type u} [inst : TopologicalSpace α] [PreconnectedSpace α] {s : Set α}, frontier s = ∅ ↔ s = ∅ ∨ s = Set.univ- Defined in
- Mathlib.Topology.Connected.Clopen
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
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
- Set.univstatement · cited by 3,945
- frontierstatement · cited by 214
- PreconnectedSpacestatement and proof · cited by 64
- isClopen_iffproof · cited by 6
- isClopen_iff_frontier_eq_emptyproof · cited by 6
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