Bulletin of the Belgian Mathematical Society - Simon Stevin

Maximal lineability of the set of continuous surjections

Nacib Gurgel Albuquerque

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Abstract

Let $m,n$ be positive integers. In this short note we prove that the set of all continuous and surjective functions from $\mathbb{R}^{m}$ to $\mathbb{R}^{n}$ contains (excluding the $0$ function) a $\mathfrak{c}$-dimensional vector space. This result is optimal in terms of dimension.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 1 (2014), 83-87.

Dates
First available in Project Euclid: 11 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1394544296

Digital Object Identifier
doi:10.36045/bbms/1394544296

Mathematical Reviews number (MathSciNet)
MR3178532

Zentralblatt MATH identifier
1296.15002

Subjects
Primary: 15A03: Vector spaces, linear dependence, rank

Keywords
lineability spaceability algebrability Peano type function

Citation

Albuquerque, Nacib Gurgel. Maximal lineability of the set of continuous surjections. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 1, 83--87. doi:10.36045/bbms/1394544296. https://projecteuclid.org/euclid.bbms/1394544296


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