Theorems · Theorem · general topology
UniformSpace.replaceTopology_eq
∀ {α : Type u_2} [i : TopologicalSpace α] (u : UniformSpace α) (h : i = u.toTopologicalSpace), u.replaceTopology h = u- Defined in
- Mathlib.Topology.UniformSpace.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- UniformSpacestatement and proof · cited by 2,040
- UniformSpace.extproof · cited by 34
- UniformSpace.replaceTopologystatement · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- ContDiffMapSupportedIn.uniformSpace_eq_iInfproof · cited by 1
- UniformConvergenceCLM.uniformSpace_eqproof · cited by 1
- ContinuousMap.uniformSpace_eq_inf_precomp_of_coverproof · cited by 1
- ContinuousMap.uniformSpace_eq_iInf_precomp_of_coverproof · cited by 0