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homogeneousSpace_exists_inj_tendsto

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Problem 13 in [Ar2013]: Is it true that every infinite homogeneous compact space contains a non-trivial convergent sequence?

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Lean 4 Statement 
theorem homogeneousSpace_exists_inj_tendsto :
    answer(sorry) ↔ ∀ (X : Type) (_ : TopologicalSpace X), ¬ Finite X → CompactSpace X →
      HomogeneousSpace X → ∃ s : ℕ → X, s.Injective ∧ ∃ a : X, Tendsto s atTop (nhds a)
ID: Paper__Homogenous__homogeneousSpace_exists_inj_tendsto
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