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Theorems · Theorem · general topology

UniformContinuous.const_smul

∀ {M : Type v} {X : Type x} {Y : Type y} [inst : UniformSpace X] [inst_1 : UniformSpace Y] [inst_2 : SMul M X]
  [UniformContinuousConstSMul M X] {f : Y → X}, UniformContinuous f → ∀ (c : M), UniformContinuous (c • f)
Defined in
Mathlib.Topology.Algebra.UniformMulAction
Cited by
3 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
UniformSpaceUniformSpaceSMulUniformContinuousConstSMul
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

UniformContinuous.mul_const' · cited by 2UniformContinuous.mul_con…UniformContinuous.const_mul' · cited by 1UniformContinuous.const_m…IsUniformInducing.uniformContinuousConstSMul · cited by 0IsUniformInducing.uniform…UniformSpace · cited by 2040UniformSpaceUniformContinuous · cited by 410UniformContinuousUniformContinuous.comp · cited by 60UniformContinuous.compUniformContinuousConstSMul · cited by 27UniformContinuousConstSMulUniformContinuousConstSMul.uniformContinuous_const_smul · cited by 4UniformContinuousConstSMu…UniformContinuous.const_smulCITED BYCITES

Cites5

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Cited by3

Results whose statement or proof uses this declaration.