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Proceedings of the American Mathematical Society

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An arcwise connected dense Hamel basis for Hilbert space


Author: Emory Hughes Merryman
Journal: Proc. Amer. Math. Soc. 26 (1970), 126-128
MSC: Primary 46.15
DOI: https://doi.org/10.1090/S0002-9939-1970-0264376-1
MathSciNet review: 0264376
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Abstract: This paper shows if $ X$ is an infinite dimensional Banach space, $ X$ contains a linearly independent arc. Also based on the continuum hypothesis, that if $ X$ is an infinite dimensional Banach space and card $ X = c$, then $ X$ contains a dense arcwise connected Hamel basis.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0264376-1
Keywords: Hamel basis, Banach space
Article copyright: © Copyright 1970 American Mathematical Society