Answered: 1. Show that if & is a function from a…

1. Show that if & is a function from a nonempty compact metric space X to itself such that d(@(x), P(y)) < d(x,y), x + y, then & has a unique fixed point.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.1: Postulates For The Integers (optional)

Problem 26E: Prove that the cancellation law for multiplication holds in Z. That is, if xy=xz and x0, then y=z.

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topology question, thanks so much for explaining

1. Show that if & is a function from a nonempty compact metric space X to itself such that
d (Ф(x), Ф(у)) < d(x, у), х#у,
then & has a unique fixed point.

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