An interesting proof of the nonexistence of a continuous bijection between ℝn and ℝ2 for n ≠ 2

Hamid Reza Daneshpajouh, Hamed Daneshpajouh, Fereshte Malek

Research output: Journal PublicationArticlepeer-review

Abstract

We show that there is no continuous bijection from ℝn onto ℝ2 for n ≠ 2 by an elementary method. This proof is based on showing that for any cardinal number β ≤ 2א 0, there is a partition of Rn (n ≥ 3) into arcwise connected dense subsets.

Original languageEnglish
Pages (from-to)125-127
Number of pages3
JournalInvolve
Volume7
Issue number2
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • arcwise connected
  • dense subset
  • homeomorphism

ASJC Scopus subject areas

  • Mathematics (all)

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