Maximal lineability of the set of Continuous Surjections

Nacib Gurgel Albuquerque

Maximal lineability of the set of Continuous Surjections

Functional Analysis 2013-04-16 v1

Authors: 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.

Keywords

lineability continuous surjections vector space dimension real Euclidean spaces

Cite

@article{arxiv.1304.3834,
  title  = {Maximal lineability of the set of Continuous Surjections},
  author = {Nacib Gurgel Albuquerque},
  journal= {arXiv preprint arXiv:1304.3834},
  year   = {2013}
}

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