A Theorem on Remainders of Topological Groups

It has been established in [7], [8], and [9] that a non-locally compact topological group G with a first-countable remainder can fail to be metrizable. On the other hand, it was shown in [6] that if some remainder of a topological group G is perfect, then this remainder is first-countable. We improve considerably this result below: it is proved that in the… (More)