Let f be a mapping from ]0,1[ to ]0, 1[ defined by f(x) = x². Then *O f has a unique fixed pointO If(x)-f(y)ls2|x-yl and f has a fixed point.O None of the choices.O If(x)-f(y)l<2|x-yl and f has no fixed point.f is said to be an open mapping iff the image by f of any open set is open. Lbe the lower limit topology generated by all unions of intervals of the form{[a,b):a,beR.asb) and let T be the Euclidean tenningman from (D

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Let f be a mapping from ]0.1[ to ]0, 1[ defined by f(x) = x². Then O f has a unique fixed point O If(x)-f(y)I<2|x-yl and f has a fixed point. O None of the choices. O If(x)-f(y)l<2|x-yl and f has no fixed point.

Let f be a mapping from ]0.1[ to ]0, 1[ defined by f(x) = x². Then O f has a unique fixed point O If(x)-f(y)I<2|x-yl and f has a fixed point. O None of the choices. O If(x)-f(y)l<2|x-yl and f has no fixed point.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 10E: For each of the following parts, give an example of a mapping from E to E that satisfies the given...

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Question

Let f be a mapping from ]0,1[ to ]0, 1[ defined by f(x) = x². Then *
O f has a unique fixed point
O If(x)-f(y)ls2|x-yl and f has a fixed point.
O None of the choices.
O If(x)-f(y)l<2|x-yl and f has no fixed point.
f is said to be an open mapping iff the image by f of any open set is open. L
be the lower limit topology generated by all unions of intervals of the form
{[a,b):a,beR.asb) and let T be the Euclidean tenning
man from (D

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