Rosicki, Witold On embeddability of cones in Euclidean spaces. (English) Zbl 0857.54015 Colloq. Math. 64, No. 1, 141-147 (1993). Let \(K_1\), \(K_2\), \(K_3\), and \(K_4\), are the well-known Kuratowski curves. By proving that the cones over these graphs are not embeddable in \(\mathbb{R}^3\), the author proves that if \(X\) is a locally connected continuum and its cone is embeddable in \(\mathbb{R}^n\), for \(n\leq 3\), then \(X\) is embeddable in \(S^{n-1}\). Finally, using Blankinship’s wild arcs lying in the \(n\)-dimensional balls, he proves that for each \(n\geq3\) a locally connected continuum \(X_n\) exists, which is not embeddable in \(\mathbb{R}^n\) but its cone is embeddable in \(\mathbb{R}^{n+1}\). At the end of the paper, an interesting question is stated: If \(X\) is a locally connected continuum with its \(n\)th cone embeddable in \(\mathbb{R}^{n+2}\), is it true that \(X\) is embeddable in \(S^2\)? Reviewer: J.Grispolakis (Chania) Cited in 1 ReviewCited in 1 Document MSC: 54C25 Embedding 54F15 Continua and generalizations Keywords:embeddability; cone of a continuum; locally connected continuum PDFBibTeX XMLCite \textit{W. Rosicki}, Colloq. Math. 64, No. 1, 141--147 (1993; Zbl 0857.54015) Full Text: DOI EuDML