On the one-to-one continuous mappings of special spaces (Q2703099)

The paper is a continuation of [ibid., 199-222 (2000; Zbl 0970.54005), see above]. Some examples and results from the previous paper are improved. For instance: (1) If \(0\leq I(X)<\infty\) and Ind\( X=0\) then for every \(0\leq n\leq I(X)\) there exists a clopen set \(X_n\) in \(X\) with \(I(X_n)=n\). (2) For \(0\leq n\leq \infty\), \(0\leq m<\infty\) there exist completely metrizable separable spaces \(X, Y\) with \(I(X)=\infty\), \(\dim X=n\), \(I(Y)=m\) such that \(X\) is finer than \(Y\) (this generalizes the case \(n=0\) where \(X\) coincides with irrationals; such a situation cannot occur for rationals).