Let X be topological space &separable.Y subset of X.Show that Y may not be separable as a subspace topology?

Answer 1

The first example on the source page listed below answers your question.

Answer 2

that's least perplexing to apply the certainty that a function is non-end if and on condition that inverse photographs of closed gadgets are closed. So enable C be closed in Y. The inverse image of C under h is the union of the inverse photographs of C under f and g. yet those are the two closed subsets of closed subspaces, so are closed in X. yet then the union is closed in X.

Answer 3

That's way to hard for us, maybe you simplify it..