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?

karthik s , 9 Years ago

Grade