f :R → Sasa continuousProve that iffunction then f is not injective.Provide a topological proof. RememberS_\omega is not metrizable (you can't useepsilon/delta definition, must use thedefinition of continuity as the preimage ofopen intervals)S_omega is the section of X by omega

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Prove that if function then f is not injective. Provide a topological proof. Remember sa continuous

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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Question

f :R → Sa
sa continuous
Prove that if
function then f is not injective.
Provide a topological proof. Remember
S_\omega is not metrizable (you can't use
epsilon/delta definition, must use the
definition of continuity as the preimage of
open intervals)
S_omega is the section of X by omega

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