Can you give me an example of a countable-dimensional normed space? I don't find anyone
2026-04-11 23:23:27.1775949807
Countable-dimensional normed spaces
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I will assume that you are talking about Hamel dimension.
Take any infinite dimensional normed linear space $Y$ and take a sequence $(x_n)$ of linearly independent vectors in it. Then $X=span (x_1,x_2,...)$ is a countable dimensional normed linear space.
Specific example: the space of all finitely non-zero sequences with the norm from $\ell^{2}$ is one such space.
Polynomials on $[0,1]$ with the sup norm is another example.