part i (ii) A topological space (X, T) is said to have the fixed point property if everycontinuous mapping of (X, T) into itself has a fixed point. Show that theonly intervals in R having the fixed point property are the closed intervals.(iii) Let X be a set with at least two points. Prove that the discrete space (X, T)and the indiscrete space (X, T') do not have the fixed-point property.(iv) Does a space which has the finite-closed topology have the fixed-pointproperty?(v) Prove that if the space (X, T) has the fixed-point property and (Y, T1) is aspace homeomorphic to (X, T), then (Y.T1) has the fixed-point property.

Name: part i (ii) A topological space (X, T) is said to have the fixed point
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Description: part i (ii) A topological space (X, T) is said to have the fixed point property if everycontinuous mapping of (X, T) into itself has a fixed point. Show that theonly intervals in R having the fixed point property are the closed intervals.(iii) Let X

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(ii) A topological space (X, T) is said to have the fixed point property if every continuous mapping of (X, T) into itself has a fixed point. Show that the only intervals in R having the fixed point property are the closed intervals.

(ii) A topological space (X, T) is said to have the fixed point property if every continuous mapping of (X, T) into itself has a fixed point. Show that the only intervals in R having the fixed point property are the closed intervals.

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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