Theorems · Definition · general topology
UniformSpace.replaceTopology
{α : Type u_2} → [i : TopologicalSpace α] → (u : UniformSpace α) → i = u.toTopologicalSpace → UniformSpace αReplace topology in a UniformSpace instance with a propositionally (but possibly not
definitionally) equal one.
- Defined in
- Mathlib.Topology.UniformSpace.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 61 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.
Cites5
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.uniformityproof · cited by 5
- UniformSpace.symmproof · cited by 1
- UniformSpace.compproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- TopologicalSpace.pseudoMetrizableSpaceUniformityproof · cited by 6
- UniformSpace.replaceTopology_eqstatement · cited by 4
- Topology.IsEmbedding.comapUniformSpaceproof · cited by 1
- PseudoMetricSpace.ofDistTopologyproof · cited by 0
- UniformSpace.replaceTopology.congr_simpstatement and proof · cited by 0