leanprover-community / leanprover-community/mathlib4
refactor: redefine metrizable and Polish spaces
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Description
New definitions:
class PseudoMetrizableSpace (X : Type*) [t : TopologicalSpace X] : Prop where
exists_countably_generated_uniformity : ∃ U : UniformSpace X,
IsCountablyGenerated (𝓤[U]) ∧ U.toTopologicalSpace = t
class MetrizableSpace (X : Type*) [TopologicalSpace X]
extends T0Space X, PseudoMetrizableSpace X : Prop where
class PolishSpace (X : Type*) [t : TopologicalSpace X] extends T0Space X, SeparableSpace X : Prop where
exists_complete_uniformity : ∃ U : UniformSpace X, IsCountablyGenerated (𝓤[U]) ∧
@CompleteSpace X U ∧ U.toTopologicalSpace = t
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start by locating the existing definitions of metrizable and Polish spaces and the code that uses them. Compare those definitions with the proposed classes in the issue, then verify that the updated definitions and their dependents compile without breaking existing topology results.
Written by the indexing model from the issue text.
Assessment
- Domain
- tooling
- Issue type
- Refactor
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 25/100