Timeline for How continuous can a bijection between line and plane be?
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Jul 1, 2018 at 21:37 | comment | added | Vesselin Dimitrov | Somewhat relevant (to my mind) is a paper, On Jordan arcs and Lipschitz classes of functions defined on them (projecteuclid.org/download/pdf_1/euclid.acta/1485889215 ), by Besicovitch and Schoenberg from 1961 in Acta Math., in which they probe the extent to which $[0,1]^2$ may be 'approximated' by an injective continuous image of $[0,1]$. It includes both positive (Theorem 1) and negative (Theorem 2) results. | |
Jul 1, 2018 at 21:10 | answer | added | James | timeline score: 17 | |
Jul 1, 2018 at 20:37 | review | First posts | |||
Jul 1, 2018 at 20:46 | |||||
Jul 1, 2018 at 20:34 | history | asked | Milo | CC BY-SA 4.0 |