Abstract
ABSTRACTLet X be a zero‐dimensional first category absolute Borel set of ambiguous class two. Then X can be given the structure of a topological group if and only if X is homogeneous and X=X x X. Thus, within the ambiguous class two, zero‐dimensional groups only occur at the low levels, and the indecomposable levels of the hierarchy of difference classes DαΣ02 in 2ω.
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