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Conjectures around homogeneous topological spaces: firstCountableTopology_of_countablyMonolithicSpace

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Statement

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

Lean statement

theorem firstCountableTopology_of_countablyMonolithicSpace :
    ∀ (X : Type) (_ : TopologicalSpace X), T2Space X → CompactSpace X →
      HomogeneousSpace X → CountablyMonolithicSpace X → FirstCountableTopology X := by
  sorry

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Openness evidence

Tagged category research open in google-deepmind/formal-conjectures at commit a64e959c32c2. Definitions used by the statement are in FormalConjectures/Paper/Homogenous.lean.

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