Dense Embeddings of Sigma-Compact, Nowhere Locally Compact Metric Spaces
Dense Embeddings of Sigma-Compact, Nowhere Locally Compact Metric Spaces
It is proved that a connected complete separable ANR $Z$ that satisfies the discrete $n$-cells property admits dense embeddings of every $n$-dimensional $\sigma$-compact, nowhere locally compact metric space $X(n \in N \cup \{ 0,\infty \} )$. More generally, the collection of dense embeddings forms a dense ${G_\delta }$-subset of the …