- #1
MathematicalPhysicist
Gold Member
- 4,699
- 372
My assignment is like this:
1.give an example of a space X and a subspace A of X s.t X satisifes Sep and A doesnt.
2.give an example of a continuous and onto function f:X->Y s.t X satisifies S1 but Y doesnt.
3.give an example of a continuous and onto function f:X->Y s.t X satisfies S2 and Y doesnt.
my answers are as follows:
1. X=R A=R-Q, is it a good example?
2.X=N, Y=N-{0}U{sqrt2} and f:X->Y f(x)=x if x in N-{0} and f(x)=sqrt2 if x=0, i think we can't find a countable set of bases for Y, not sure though.
3. didn't do it so far, any hints?
1.give an example of a space X and a subspace A of X s.t X satisifes Sep and A doesnt.
2.give an example of a continuous and onto function f:X->Y s.t X satisifies S1 but Y doesnt.
3.give an example of a continuous and onto function f:X->Y s.t X satisfies S2 and Y doesnt.
my answers are as follows:
1. X=R A=R-Q, is it a good example?
2.X=N, Y=N-{0}U{sqrt2} and f:X->Y f(x)=x if x in N-{0} and f(x)=sqrt2 if x=0, i think we can't find a countable set of bases for Y, not sure though.
3. didn't do it so far, any hints?