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Is the ideal $I = \{f \mid f (0) = 0\}$ in the ring $C [0, 1]$ of all continuous real valued functions on the interval $[0, 1]$ a maximal ideal?

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    Why do you ask? What do you think? What have you tried?2012-12-30
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    yes,infact I={f:f(c)=0} are the all possible maximal ideals2012-12-30
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    **Hint:** Try to determine the quotient $C[0,1]/I$ using the map $\phi: g\mapsto g(0)$. What is $\ker \phi$? What is ${\rm Im}~\phi$?2012-12-30
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    where is the compactness of [0,1] used?2012-12-30
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    Why do you think compactness would be used, @K.Ghosh?2012-12-30
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    in C(0,1) does this hold? i don't know2012-12-30
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    @K.Ghosh, Compactness is needed for the statement that every max ideal is of the form $I_c = \{f: f(c) = 0\}$, not this one.2012-12-30
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    This question is contained in http://math.stackexchange.com/questions/375400/maximal-ideals-in-the-ring-of-real-functions-on-0-12013-05-26

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