#62

Let R be the set of real numbers with the topology generated by the basis {[a,b): a <b, a,b in R} If X is the subset [0,1] of R, which of the following must be true

1.x is compact

2.x is hausdorff

3.x is connected

(A) I only

(B) II only

(C) III only

(D) I AND II

(E) II and III

Hi, can anyone give a quick crash course on what it means to be Hausdorff?

Also, isn't [0,1] close and bounded and therefore compact?

Also, isn't [0,1] connected?

Thanks for clearing my deep misunderstandings on topology! :S