- #1
Pippi
- 18
- 0
I want to come up with examples that finite complement topology of the reals R is not Hausdorff, because by definition, for each pair x1, x2 in R, x1 and x2 have some disjoint neighborhoods.
My thinking is as follows: finite complement topology of the reals R is a set that contains open sets of the form, (- inf, a1) U (a1, a2) U ... U (an, inf). The complement of an open set is the finite elements {a1, a2, ... an}. However, any two points I pick out of any open set have disjoint neighborhoods. How is it possible?
My thinking is as follows: finite complement topology of the reals R is a set that contains open sets of the form, (- inf, a1) U (a1, a2) U ... U (an, inf). The complement of an open set is the finite elements {a1, a2, ... an}. However, any two points I pick out of any open set have disjoint neighborhoods. How is it possible?