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arXiv · 2406.04078

How many sprays cover the space?

Alessandro Andretta·Ivan Izmestiev
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Abstract

For all $d \geq 3$ we show that the cardinality of $ \mathbb{R} $ is at most $\aleph_n $ if and only if $ \mathbb{R}^d $ can be covered with $ ( n + 1 ) ( d - 1 ) + 1 $ sprays whose centers are in general position in a hyperplane. This extends previous results by Schmerl when $ d = 2 $.

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Alessandro Andretta, Ivan Izmestiev. 2024-06-06. How many sprays cover the space?. https://doi.org/10.2140/pjm.2026.341.1

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