×

zbMATH — the first resource for mathematics

On rigid subsets of some manifolds. (English) Zbl 0706.54026
K. Borsuk proved that if every homeomorphism preserving length of arcs, between open connected subsets of a Euclidean space, is an isometry [Glasnik Mat. 16(36), 307-311 (1981; Zbl 0494.54027)]. The present paper generalizes the result to certain finite-dimensional manifolds and shows that it is not true for the Hilbert space.
Reviewer: M.Hušek

MSC:
54E40 Special maps on metric spaces
57N15 Topology of the Euclidean \(n\)-space, \(n\)-manifolds (\(4 \leq n \leq \infty\)) (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI