infinite dimentional subspace need not be closed

nwl

New member
Let X=C[O,1] and Y=span($X_{0},X_{1},···$), where $X_{j}={t}^{i}$, so that Y is the set of all polynomials. Y is not closed in X.

Last edited by a moderator:

topsquark

Well-known member
MHB Math Helper
Let X=C[O,1] and Y=span(x\_{0},x\_{1},···), where X\_{j}={t}^{i}, so that Y is the set of all polynomials. Y is not closed in X.