Mathlib Map

Theorems · Theorem · general topology

uniformContinuous_const

∀ {α : Type ua} {β : Type ub} [inst : UniformSpace α] [inst_1 : UniformSpace β] {b : β}, UniformContinuous fun x => b
Defined in
Mathlib.Topology.UniformSpace.Defs
Cited by
21 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceUniformSpace
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Around this declaration

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

UniformContinuous.inv · cited by 3UniformContinuous.invUniformContinuous.neg · cited by 3UniformContinuous.negUniformContinuous.sub_const · cited by 1UniformContinuous.sub_con…UniformContinuous.add_const · cited by 1UniformContinuous.add_con…FiniteDimensional.of_totallyBounded_nhds · cited by 1FiniteDimensional.of_tota…UniformContinuous.const_add · cited by 1UniformContinuous.const_a…UniformContinuous.const_mul · cited by 1UniformContinuous.const_m…CauchySeq.add_const · cited by 1CauchySeq.add_constUniformContinuous.div_const · cited by 1UniformContinuous.div_con…uniformity_translate_add · cited by 1uniformity_translate_adduniformity_translate_mul · cited by 1uniformity_translate_mulUniformContinuous.mul_const · cited by 1UniformContinuous.mul_con…Finset.uniformContinuous_prod · cited by 0Finset.uniformContinuous_…Finset.uniformContinuous_sum · cited by 0Finset.uniformContinuous_…CauchySeq.const_add · cited by 0CauchySeq.const_addUniformSpace · cited by 2040UniformSpaceUniformContinuous · cited by 410UniformContinuousuniformContinuous_of_const · cited by 4uniformContinuous_of_constuniformContinuous_constCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by21

Results whose statement or proof uses this declaration.