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#### bw0young0math

##### New member

- Jun 14, 2013

- 27

Please help me.

Here is the problem.

X: topological space&T2(Hausdorff)

D: dense subet of X

f:X→Y is continuous function and

restriction fuction of f to D i.e., f(D) is embedding fuction.

Show that f(X-D)<Y-f(D) (<means set inclusion. i.r., Y -f(D) includes f(X-D). )

I wanted to solve it as using Reduction absurdity.

Thus I assumed that there exists a y in f(X-D) but not in Y-f(D).

Therefore I supposed that f(X-D) < f(D).

then.. how can I solve it with many conditions above?

Please help me