Abstract:In this note, we prove that any ``bounded'' isometries of separable metric spaces can be represented as restrictions of linear isometries of function spaces $C(Q)$ and $C(\Delta)$, where $Q$ and $\Delta$ denote the Hilbert cube $[0,1]^{\infty}$ and a~Cantor set, respectively.
Keywords: linear extension of isometry; theorem of Banach and Mazur; Hilbert cube; Cantor set
DOI: DOI 10.14712/1213-7243.015.109
AMS Subject Classification: 54C35 46B04 54H20