Dense embeddings of nowhere locally compact separable metric spaces
Let all spaces be separable metric. \textit{D. W. Curtis} [ibid. 16, 253-257 (1983; Zbl 0516.54013)] proved that every \(\sigma\)-compact space can be densely imbedded in Hilbert space. In this important paper, via a very interesting technique, the author extends this result. He proes that X is nowhere locally compact if and only if X imbeds densely in Hilbert space; as a consequence, every nowhere locally compact space can be densely imbedded in the Hilbert cube. In addition, X is nowhere locally compact and of dimension at most n if and only if X imbeds densely in the n- dimensional Menger-Nöbeling space; as a consequence, every nowhere locally compact space that is at most n-dimensional embeds densely in the n-dimensional Menger space.
scientific article; zbMATH DE number 4013508
scientific article