On J. Nagata's universal spaces
The author develops some interesting analogues of the classical Hurewicz- Kuratowski theorem that for a separable n-dimensional metric space X, the set of (homeomorphic) embeddings of X into \(I^{2n+1}\) is dense in the space of all continuous mappings from X into this universal space [cf. \textit{W. Hurewicz} and \textit{H. Wallman}, Dimension theory (1948; Zbl 0036.125), Theorem V3, p. 60]. J. Nagata has established universal spaces for n-dimensional or countable-dimensional spaces of weight \(\tau\) in the class of metrizable spaces (resp. strongly metrizable spaces). The author proves that in each case the set of embeddings is dense in the space of all continuous mappings into the relevant universal space of Nagata.
scientific article; zbMATH DE number 4007231
scientific article