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arXiv · 2010.01983

Transfinite dimensions

Gerald Kuba
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Abstract

Let H be a Hilbert space and let F be the family of all countable subsets of an orthonormal basis of H. We show that if F is infinite then F is equipollent with every linear basis of the vector space H. In doing so we also present a short proof of the Erd\"os-Kaplansky theorem more natural and much easier than the one by Bourbaki.

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Gerald Kuba. 2020-09-22. Transfinite dimensions. https://arxiv.org/abs/2010.01983

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