1. Let (X, (,)) be an inner product space. Show that the inner product (,): XxX → Cis 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 aclosed subset of X.===

Answered: 1. Let (X, (,)) be an inner product…

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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Question

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.
===

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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. ===