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arXiv · 2606.13195

Some results about spaceability in function spaces

Andreas Debrouwere
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Abstract

We investigate two problems concerning spaceability in function spaces. First, we study the spaceability of sets of nowhere regular periodic functions, for various notions of regularity, including H\"older regularity and real analyticity. Second, we show that the set of real analytic functions is spaceable in $C((0,1))$. Moreover, we provide a complete characterization of the closed subspaces of $C((0,1))$ consisting of real analytic functions. Our work solves several open questions posed by Bernal-Gonz\'alez et al. [4, 5, 6].

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Andreas Debrouwere. 2026-06-11. Some results about spaceability in function spaces. https://arxiv.org/abs/2606.13195

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