Maximal lineability of the set of Continuous Surjections

2013/04/13 by Nacib Gurgel Albuquerque, Albuquerque, Nacib Gurgel
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1304.3834

arxiv created 2013/04/13 · arxiv updated 2013/04/16

Abstract

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

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