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Sudhanshu Ranjan posted an Question
August 18, 2020 • 06:28 am
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30 points
30 points
- CSIR NET
- Mathematical Sciences
Show that the ring of all continuous functions from [0,1] into r contains some non zero functions which are units, some are zero divisiors and some are neither
Show that the ring of all continuous functions from [0,1] into R contains some non zero functions which are units, some are zero divisiors and some are neither units nor zero divisiors
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Shashi ranjan sinha![best-answer]()
if g is not zero at x=1/2 , then by neighborhood property of continuous function, there exist an open interval I containing 1/2 such that g assumes non zero values at all points of I . but this contradicts the fact that g is non zero only at 1/2. Hence our assumption is wrong and so g must be zero at 1/2 so that g becomes zero function