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Class 9 Homework-

Let R=C([0,1]) be the ring of continuous real-valued functions on the interval [0,1]. Let T[0,1], and let

   I(T)={fR:f(x)=0xT} .

(i) Prove that I(T) is an ideal of R.

(ii) If x[0,1] and mx=I({x}), show that R/MxR, and hence Mx is a maximal ideal of R.




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