Problem 6. Let X be a normed space. (a) Find all subspaces of X which are contained in some ball B(a; r) of X. (b) Find all subspaces of X which contain some ball B(ro; p) of X.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
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Problem 6.
Let X be a normed space.
(a) Find all subspaces of X which are contained in some ball B(a; r) of X.
(b) Find all subspaces of X which contain some ball B(ro; P) of X.
Transcribed Image Text:Problem 6. Let X be a normed space. (a) Find all subspaces of X which are contained in some ball B(a; r) of X. (b) Find all subspaces of X which contain some ball B(ro; P) of X.
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