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Theorems · Theorem · general topology

IsCompact.exists_cthickening_subset_open

∀ {α : Type u} [inst : PseudoEMetricSpace α] {s t : Set α},
  IsCompact s → IsOpen t → s ⊆ t → ∃ δ, 0 < δ ∧ Metric.cthickening δ s ⊆ t

If s is compact, t is open and s ⊆ t, some cthickening of s is contained in t.

Defined in
Mathlib.Topology.MetricSpace.Thickening
Cited by
4 results in Mathlib
Foundations
Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpace

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