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

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First steps

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  3. Fork the repository and make your change on a branch.
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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

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