Rajkov remainder and other group-remainders of a topological group
The paper is a study of dense subgroups of topological groups and their remainders. Recall that \(X\) is a Lindelöf \(p\)-space, if there exists a perfect map \(f:X\to M\) of \(X\) onto a separable metrizable space \(M\). If separability of \(M\) is omitted in the above definition, then \(X\) is called a paracompact \(p\)-space. If \(G\) is a dense subgroup of a topological group \(B\), then \(X=B\setminus G\) is called a \(g\)-remainder of \(G\) and \(B\) is a group extension of \(G\). The authors establish that, for any topological group \(G\), if \(X\) is a Lindelöf \(g\)-remainder of \(G\) which contains a compact subspace of countable character in \(X\), then both \(G\) and \(X\) are Lindelöf \(p\)-spaces. Besides, any \(g\)-remainder of \(G\) is a Lindelöf \(p\)-space. It is also proved that if some non-empty \(g\)-remainder of \(G\) is a paracompact \(p\)-space, then \(G\) is itself a paracompact \(p\)-space.
scientific article; zbMATH DE number 6893994