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countablyMonolithicSpace_exists_nhds_generated_countable

Specification

Problem 17 in [Ar2013]: Is it true that every ω-monolithic compact space contains a point with a first countable neighborhood basis?

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Lean 4 Statement 
theorem countablyMonolithicSpace_exists_nhds_generated_countable :
    answer(sorry) ↔ ∀ (X : Type) (_ : TopologicalSpace X), CompactSpace X →
      CountablyMonolithicSpace X → ∃ x : X, (𝓝 x).IsCountablyGenerated
ID: Paper__Homogenous__countablyMonolithicSpace_exists_nhds_generated_countable
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