Discrete Algebraic Methods

A cover of the neutral element 1U is (1U, 1U), a cover of x0 is (1U , x0), and a cover of xi with i ≥ 1 is given by (xi , t); this is true because for all x ∈ UX, we have

Thus, in all cases ψ(y, z)x = ψ((y, z) x̂).

7.17. We use the notation from the proof from Theorem 7.41. We define a partial mapping ψ: (UN × Mc)N#×U1 × N# × U1 → M, and show that it is a covering. The elements of (UN × Mc)N#×U1 are written as pairs of mappings (f, g) with f : N# × U1 → UN and g : N# × U1 → Mc. For (f, g, x, e) ∈ (UN × Mc)N#×U1 × N# × U1 with x ∈ N# and e ∈ U