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8. A space has "the fixed point property" if every continuous function f: X → Y leaves at least one fixed point, i.e. there exists such that x in X such that f(x)=x. Prove that the fixed point property is a topological property..

8. A space has "the fixed point property" if every continuous function f: X → Y leaves at least one fixed point, i.e. there exists such that x in X such that f(x)=x. Prove that the fixed point property is a topological property..

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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SOLVE STEP BY STEP IN DIGITAL FORMAT ジッッシÜ ♡み A A * E * ?! ?? !! ? ?! ¿¡ !?! W X I Q X X X X X X ● 8. A space has "the fixed point property" if every continuous function f: X → Y leaves at least one fixed point, i.e. there exists such that x in X such that f(x)=x. Prove that the fixed point property is a topological property..
Transcribed Image Text:SOLVE STEP BY STEP IN DIGITAL FORMAT ジッッシÜ ♡み A A * E * ?! ?? !! ? ?! ¿¡ !?! W X I Q X X X X X X ● 8. A space has "the fixed point property" if every continuous function f: X → Y leaves at least one fixed point, i.e. there exists such that x in X such that f(x)=x. Prove that the fixed point property is a topological property..
Expert Solution
Step 1: Given.

Given: 8. Suppose X is any set and f:X→X is a continuous function. The point x∈X is said to be fixed point of f if fx=x.

To show: Fixed point property is a topological property.

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