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firstCountableTopology_of_countablyMonolithicSpace

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Problem 15 in [Ar2013]: Is every homogeneous ω-monolithic compact space first countable?

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Lean 4 Statement 
theorem firstCountableTopology_of_countablyMonolithicSpace :
    answer(sorry) ↔ ∀ (X : Type) (_ : TopologicalSpace X), CompactSpace X → HomogeneousSpace X →
      CountablyMonolithicSpace X → FirstCountableTopology X
ID: Paper__Homogenous__firstCountableTopology_of_countablyMonolithicSpace
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