Equivalents of the Axiom of Choice in Algebraic Topology

Question

I've read on n-Category Café that the following statements are equivalent:

1. The Axiom of Choice
2. For any discrete set $X$ and any group $G$, the cohomology $H^{1}(X,G)$ vanishes.

I was wondering what are the others equivalences of the axiom of choice in algebraic topology of 'that kind'.