Notes on Remainders of Paratopological Groups

In this paper, it is proved that a non-locally compact paratopological group G has a remainder which is a p-space if and only if G is either a Lindelof p-space or a sigma-compact space. We show that if G is a non-locally compact paratopological group with a compactification bG such that the remainder bG \ G is locally metrizable, then both G and bG are separable and metrizable. It is proved that if G is a cosmic paratopological group with a paracompact remainder, then G is separable and metrizable.