1. Let (X, (,)) be an inner product space. Show that the inner product (,): XxX → C is continuous, that is, whenever the sequences In → x and yn y in X, we have (In, Yn) → (x, y). From this show that if A is a subset of X, then A+ = {x EX: xly, for all y € A} is a closed subset of X. ===
1. Let (X, (,)) be an inner product space. Show that the inner product (,): XxX → C is continuous, that is, whenever the sequences In → x and yn y in X, we have (In, Yn) → (x, y). From this show that if A is a subset of X, then A+ = {x EX: xly, for all y € A} is a closed subset of X. ===
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.2: Integral Domains And Fields
Problem 16E: Prove that if a subring R of an integral domain D contains the unity element of D, then R is an...
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