On cardinal invariants of continuous images of topological groups (Q1310446)

Sufficient conditions on a topological space \(X\) are indicated in order that the character \(\chi(p,X)\) and the tightness \(t(p,X)\) coincide at every point \(p\in X\). We state the main result: Theorem 1. If a compact space \(X\) is a continuous image of a dense subset in a product of \(\sigma\)-compact topological groups, then \(\chi(p,X)=t(p,X)\) for every point \(p\in X\). The paper contains also some more general assertions than theorem 1. At the end the author poses three open problems. We mention here Question 3: Suppose there exists a continuous mapping of a dense subspace of a \(\sigma\)-compact topological group \(H\) onto a Tychonoff cube \(I^ \tau\), \(\tau>\aleph_ 0\). Is there a continuous mapping of \(H\) onto \(I^ \tau\)?