Theorems · Theorem · general topology

ContinuousMap.dist_lt_of_dist_lt_modulus

∀ {α : Type u_1} {β : Type u_2} [inst : PseudoMetricSpace α] [inst_1 : CompactSpace α] [inst_2 : PseudoMetricSpace β]
  (f : C(α, β)) (ε : ℝ) (h : 0 < ε) {a b : α}, dist a b < f.modulus ε h → dist (f a) (f b) < ε

Defined in

Mathlib.Topology.ContinuousMap.Compact

Cited by

0 results in Mathlib

Foundations

Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceCompactSpacePseudoMetricSpace