A note on transfinite inductive dimensions in topological groups (Q1314679)

Let \(X\) be a homogeneous normal space. The author proves among other things that if the large transfinite inductive dimension \(\text{trInd }X\) of \(X\) is defined then \(\text{ind } X\) is finite or \(X\) is countably compact. If \(X\) is a (normal) topological group for which \(\text{trInd }X\) is defined then \(\text{ind }X\) is finite. Some interesting open problems are posed.