fundamentalGroupMulEquivOfPathConnected

English

For path-connected X, fundamental groups at two points are MulEquiv.

Русский

Для связного по пути пространства X группы ФундamentalGroup(X,x0) и ФундamentalGroup(X,x1) гомоморфны как MulEquiv.

LaTeX

$$$$ [PathConnectedSpace X] \\Rightarrow \\operatorname{FundamentalGroup}(X,x_0) \\cong_* \\operatorname{FundamentalGroup}(X,x_1). $$$$

Lean4

/-- The fundamental group of a path connected space is independent of the choice of basepoint. -/
def fundamentalGroupMulEquivOfPathConnected [PathConnectedSpace X] : FundamentalGroup X x₀ ≃* FundamentalGroup X x₁ :=
  fundamentalGroupMulEquivOfPath (PathConnectedSpace.somePath x₀ x₁)

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