Remainders and cardinal invariants (Q2435268)

Let \(X\) be a Tychonoff topological space. A \textit{remainder} of \(X\) is the subspace \(bX\setminus X\) of a Hausdorff compactification \(bX\) of \(X\). The authors consider the relationship between cardinal functions of some topological spaces, especially non-locally compact spaces and nowhere locally compact spaces, and the properties of their remainders. Several results involving topological groups are proved. The authors highlight the following ones: (1) If a non-locally compact homogeneous space \(X\) is locally ccc and \(X\) has a remainder with a locally point-countable base, then \(w(X)\leq 2^{\omega}\); (2) If a nowhere locally compact space \(X\) with locally a \(G_{\delta}\)-diagonal has a remainder that is a paracompact \(p\)-space, then \(w(X)=\omega\); (3) If a non-locally compact paratopological group \(G\) has a developable remainder \(Y\), then \(nw(G)=\pi w(G)=\pi w(Y)=\omega\); (4) If a non-locally compact paratopological group \(G\) has a remainder \(Y\) with a point-countable base, then \(w(G)=w(Y)=\omega\); (5) If a semitopological group \(H\) is \(r\)-equivalent to a non-locally compact semitopological group \(G\) that has a countable base, then \(w(H)=\omega\).