that whether ivi(b) Let U, T be usual and cofinite topologies on se:t of real numbers Rand f be a map from R into R such that f(x)=1x-21 for any xER, showt.hat wheter f is U-T continuous or not and T---U continuous or not.(c) Let f be a map from a space(X, T).into a space (Y, t) and t, Tzsuch thatTSt and tS T,, show that whether if f is T,---t open map then f is t---t open map then f is t --- Topen map or not.open map or not, and if f is r---てくててーでcfennaPうてーモ。てこて。To Hoad of Dept.

As per our guidelines we are supposed to answer only first question. So i have solve question (b)…

Answered: (b) Let U, T be usual and cofinite…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 24E

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(b) Let U, T be usual and cofinite topologies on se:t of real numbers R and f be a map from R into R such that f(x)=1x-21 for any xER, show t.hat wheter f is U-T continuous or not and t--U continuous or not. Such that