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Theorems · Theorem · general topology

Set.relatively_discrete_of_finite

∀ {α : Type u_1} [inst : EMetricSpace α] {s : Set α} [Finite ↑s], ∃ C > 0, ∀ x ∈ s, ∀ y ∈ s, x ≠ y → C ≤ edist x y
Defined in
Mathlib.Topology.MetricSpace.Infsep
Cited by
1 results in Mathlib
Foundations
Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
EMetricSpaceFinite
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Around this declaration

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Set.Finite.relatively_discrete · cited by 0Finite.relatively_discreteSet · cited by 53352SetENNReal · cited by 9879ENNRealSet.Elem · cited by 7166Set.ElemFinite · cited by 3029FiniteEDist.edist · cited by 735EDist.edistEMetricSpace · cited by 242EMetricSpaceSet.einfsep_pos_of_finite · cited by 4Set.einfsep_pos_of_finiteSet.einfsep_pos · cited by 1Set.einfsep_posSet.relatively_discrete_of_fi…CITED BYCITES

Cites8

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Cited by1

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