Abstract
This chapter is a rigorous introduction to linear spaces, but with a strong emphasis on infinite-dimensional linear spaces. No prior knowledge of linear spaces is assumed, so that all definitions and proofs are included, but some mathematical maturity is assumed, dictating the level of detail given. In particular, all results (e.g., existence of dimension) are given in full generality using Zorn’s Lemma.
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Alabiso, C., Weiss, I. (2021). Linear Spaces. In: A Primer on Hilbert Space Theory. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-67417-5_2
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DOI: https://doi.org/10.1007/978-3-030-67417-5_2
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