On isometric embeddings of compact metric spaces of a countable dimension (Q388027)

The class of spaces considered is the class of metric separable spaces. The result of the first author [Topology Appl. 160, No. 11, 1271--1283 (2013; Zbl 1282.54013)], where the covering dimension was in place, is extended to separable metric spaces of (transfinite) inductive dimension ind \(\leq \alpha \in \omega^+\). An embedding \(f:X\to Y\) is called isometry (isometric embedding) if it preserves the distance between points, i.e. \(d_Y(f(x),f(x')) = d_X(x,x')\) for all \(x,x'\in X\). The result says, that there exists a complete separable metric space \(Y\) of transfinite dimension ind \(\leq \alpha \in \omega^+\) containing isometrically all compact metric spaces of transfinite dimension ind \(\leq \alpha \in \omega^{+}\)NEWLINENEWLINEAs a corollary one obtains the result of the above quoted paper. Compared with known cases, the stress is on completeness of \(Y\).