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2014 An interesting proof of the nonexistence of a continuous bijection between $\mathbb{R}^n$ and $\mathbb{R}^2$ for $n\neq 2$
Hamid Daneshpajouh, Hamed Daneshpajouh, Fereshte Malek
Involve 7(2): 125-127 (2014). DOI: 10.2140/involve.2014.7.125

Abstract

We show that there is no continuous bijection from n onto 2 for n2 by an elementary method. This proof is based on showing that for any cardinal number β20, there is a partition of Rn (n3) into β arcwise connected dense subsets.

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Hamid Daneshpajouh. Hamed Daneshpajouh. Fereshte Malek. "An interesting proof of the nonexistence of a continuous bijection between $\mathbb{R}^n$ and $\mathbb{R}^2$ for $n\neq 2$." Involve 7 (2) 125 - 127, 2014. https://doi.org/10.2140/involve.2014.7.125

Information

Received: 3 June 2012; Revised: 27 November 2012; Accepted: 1 December 2012; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1282.54012
MathSciNet: MR3133714
Digital Object Identifier: 10.2140/involve.2014.7.125

Subjects:
Primary: 54-XX
Secondary: 54CXX

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.7 • No. 2 • 2014
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