Topology
Topology
2nd Edition
ISBN: 9780134689517
Author: Munkres, James R.
Publisher: Pearson,
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Chapter 3.24, Problem 3E

Let f : X X be a continuous. Show that if X = [ 0 , 1 ] , there is a point x such that f ( x ) = x . The point x is called a fixed point of f . What happens if X equals [ 0 , 1 ) or ( 0 , 1 ) ?

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