Thread: Hausdorff

how would I prove a subset x of Euclidean space with the usual topology is Hausdorff?
I know that I need to show that for a pair of distinct points a,b in x there exists two open sets such that a in u and b in v and these two sets have no elements in common.....
Not sure how to proceed...!

Originally Posted by bigdoggy

how would I prove a subset x of Euclidean space with the usual topology is Hausdorff?
I know that I need to show that for a pair of distinct points a,b in x there exists two open sets such that a in u and b in v and these two sets have no elements in common.....
Not sure how to proceed...!

If a and b are distinct points then d(a,b)> 0. Look at the neighborhood centered on a with radius d(a,b)/3 and the neighborhood centered on b with radius d(a,b)/3.