## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Maximal lineability of the set of continuous surjections

Nacib Gurgel Albuquerque

#### 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

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

#### 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