polishSpace — Mathlib

English

Pulling back a Polish topology along an equivalence yields a Polish space.

Русский

Перекладывая полиш-структуру по эквивалентности, получаем снова полиш-пространство.

LaTeX

$$$$\\\\text{If } f: α \\simeq β, \\text{ then } α \\text{ with the induced topology from } β \\text{ is Polish}. $$$$

Lean4

/-- A closed subset of a Polish space is also Polish. -/
theorem _root_.IsClosed.polishSpace [TopologicalSpace α] [PolishSpace α] {s : Set α} (hs : IsClosed s) :
    PolishSpace s :=
  hs.isClosedEmbedding_subtypeVal.polishSpace

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