- Thread starter
- #1
bw0young0math
New member
- Jun 14, 2013
- 27
Hello. My friend asked me thos problem today, but I couldn't.
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
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