Topological groups homeomorphic to products of discrete spaces

AbstractWe give necessary and sufficient conditions for a topological group to be homeomorphic to a product of the form Nκ × Dτ, where κ and τ are infinite cardinals and N and D denote countable (infinite) and two-point discrete spaces respectively. These conditions are purely topological: (a) zero-dimensionality in the sense of dim; and (b) being an absolute extensor in the dimension zero (briefly, an AE(0) space)