An arcwise connected dense Hamel basis for Hilbert space

Emory Hughes Merryman
1970 Proceedings of the American Mathematical Society  
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.
doi:10.1090/s0002-9939-1970-0264376-1 fatcat:rgcp42rqzjenla6icyipeaaplu