Q2: a) Let f be a map from a set X into a space (Y,T) andT' {Us XaV e T,U f"(V).show that T is smallest topology on X,makes f continuous.b) Let T be a co finite topology on a set of reai numbers R and f: R →R be a mapsuch that f(x) =k + 2/, show that whether f is T-T continuous or not.

Given: Assume that f is a map from a set X to a space (Y,T), and that Tι=U⊆X|∃V∈T,U=f-1V.…

Answered: Q2: a) Let f be a map from a set X iato…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Q2: a) Let f be a map from a set X iato a space (Y,T) and T'- {Uc xaV eT, U=f"(vshow that T is smallest topology on X,makes f continuous. b) Let T be a co finite topology on a set of reai numbers R and f:R →R be a mnap Sueh that fx) =-k+ 2, show that whether f is T-T continuous or not.