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we know that, “If X is a complete metricspace and Y is a subspace of X. then Y is complte iff Y is closed”. my question is, suppose my X=R and Y=[0,1) and define a cauchy sequence {1/n} in Y and which is convergent in Y with limit 0 in Y, hence Y is complete.according to theorem Y should be closed but here Y is not closed. can anyone give some suggestion about it?

we know that,
“If X is a complete metricspace and Y is a subspace of X. then Y is complte iff Y is closed”.
my question is, suppose my X=R and Y=[0,1) and define a cauchy sequence {1/n} in Y and which is convergent in Y with limit 0 in Y, hence Y is complete.according to theorem Y should be closed but here Y is not closed. can anyone give some suggestion about it?

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1 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
2 years ago
Dear student

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