map_coclosedCompact — Mathlib

English

A homeomorphism preserves punctured neighborhoods: map h (nhdsWithin x without {x}) = nhdsWithin h(x) without {h(x)}.

Русский

Гомеоморфизм сохраняет окружности без точки: map h (nhdsWithin x без {x}) = nhdsWithin h(x) без {h(x)}.

LaTeX

$$$map\\, h\\, (nhdsWithin\\, x\\, (\\\\{x\\\\}^{c})) = nhdsWithin\\, (h x)\\, (\\\\{h x\\\\}^{c})$$$

Lean4

@[simp]
theorem map_coclosedCompact (h : X ≃ₜ Y) : map h (coclosedCompact X) = coclosedCompact Y := by
  rw [← h.comap_coclosedCompact, map_comap_of_surjective h.surjective]

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