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 | References | Similar Articles | Additional Information
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.
- Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368 F. Hausdorff, Zur Theorie der linearen metrischen Räume, J. Reine Angew. Math. 167 (1932), 294-311.
- Gordon G. Johnson, A crinkled arc, Proc. Amer. Math. Soc. 25 (1970), 375–376. MR 259574, DOI https://doi.org/10.1090/S0002-9939-1970-0259574-7
- G. G. Johnson, Hilbert space problem four, Amer. Math. Monthly 78 (1971), 525–527. MR 285896, DOI https://doi.org/10.2307/2317762
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Keywords:
Hamel basis,
Banach space
Article copyright:
© Copyright 1970
American Mathematical Society