Abstract
In this paper, it is shown that if X is homeomorphic to the topological sum of a Tychonoff space Y and a discrete space D, then FP2(X) is locally compact if and only if FP2(Y) is locally compact. Especially, the space FP2(X) is locally compact at its every point distinct from the identity e if X is homeomorphic to the topological sum of a compact space and a discrete space. Finally, a few questions about free paratopological groups are posed.
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