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0dd3af4 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | import Mathlib
namespace OAI
namespace UniversalFInfinity
universe u
def HasTypeFInfinity (G : Type u) [Group G] : Prop :=
∃ (X : Type u) (_ : TopologicalSpace X) (_ : T2Space X)
(_ : ConnectedSpace X) (cw : Topology.CWComplex (Set.univ : Set X)),
(∀ n : ℕ, Finite (cw.cell n)) ∧
(∃ x : X, Nonempty (FundamentalGroup X x ≃* G)) ∧
∃ (E : Type u) (_ : TopologicalSpace E) (_ : ContractibleSpace E)
(p : E → X), Function.Surjective p ∧ IsCoveringMap p
end UniversalFInfinity
end OAI
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