3) Let {rn : n e N} be a basis in a normed space X. Show that X is not a Banach space. (Hint: Apply Baire's Lemma to the subspaces En = span{r1,12,...,In})
3) Let {rn : n e N} be a basis in a normed space X. Show that X is not a Banach space. (Hint: Apply Baire's Lemma to the subspaces En = span{r1,12,...,In})
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 4AEXP
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