GenLoop — Mathlib

English

The loopHomeo at i sends p to a loop whose underlying evaluation equals toLoop i p.

Русский

LoopHomeo в i переводит p в петлю, чье осн. значение равняется toLoop i p.

LaTeX

$$GenLoop.loopHomeo i p evaluated equals GenLoop.toLoop i p$$

Lean4

/-- The `n`-dimensional generalized loops based at `x` in a space `X` are
  continuous functions `I^n → X` that sends the boundary to `x`.
  We allow an arbitrary indexing type `N` in place of `Fin n` here. -/
def GenLoop : Set C(I^N, X) :=
  {p | ∀ y ∈ Cube.boundary N, p y = x}

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