3.1. Let X be a vector space and d a metric on X. Show that a pair (X, d) is a metric vector space if for sequences (x,) and (yn) of vectors in X and sequences (An) of scalars in F, these conditions hold: (a) Xn - x, Yn -y imply (xn + Yn) (x +y), (b) - x imply Anan - Ar.
3.1. Let X be a vector space and d a metric on X. Show that a pair (X, d) is a metric vector space if for sequences (x,) and (yn) of vectors in X and sequences (An) of scalars in F, these conditions hold: (a) Xn - x, Yn -y imply (xn + Yn) (x +y), (b) - x imply Anan - Ar.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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