2023/08/22 by Farah, Ilijas, Marshall-Milne, Jeffrey
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2308.11826
Within the framework of Zermelo-Fraenkel set theory without the Axiom of Choice, we establish equivalents to the assertion "the union of a countable collection of finite sets is countable" in the context of metric spaces, probability theory, and Hilbert spaces. The categorical principle underlying these equivalences is identified.