More on remainders close to metrizable spaces (Q870236)

The author continues his study of remainders in compactifications and generalized metrizability properties. He proves among other things that if \(X\) is a non-locally compact topological group, and \(bX\) is a compactification of \(X\) such that \(Y=bX\setminus X\) has a \(G_\delta\)-diagonal or a point-countable base, then both \(X\) and \(Y\) are separable and metrizable. A non-locally compact topological group may have a first countable remainder without being separable, which shows that the obtained results are close to being optimal. The author also notes that his results do not extend to paratopological groups.