Theorems · Theorem · general topology
Set.Countable.isTotallyDisconnected
∀ {X : Type u_1} [inst : MetricSpace X] {s : Set X}, s.Countable → IsTotallyDisconnected sCountable subsets of metric spaces are totally disconnected.
- Defined in
- Mathlib.Topology.Separation.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpace
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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
- Set.Elemproof · cited by 7,166
- MetricSpacestatement and proof · cited by 1,684
- Countableproof · cited by 633
- Set.Countablestatement and proof · cited by 545
- IsTotallyDisconnectedstatement · cited by 14
- totallyDisconnectedSpace_subtype_iffproof · cited by 1
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