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arXiv · 1304.3834

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.

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Nacib Gurgel Albuquerque. 2013-04-13. Maximal lineability of the set of Continuous Surjections. https://arxiv.org/abs/1304.3834

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