Question

Let T be the half-open interval topology for R, defined in Exercise 4.6.

Show that (R,T) is a T₄ - space.

Exercise 4.6

The intersection of two half-open intervals of the form [a,b) is either empty or a half-open interval. Thus the family of all unions of half-open intervals together with the empty set is closed under finite intersections, hence forms a topology, which has the half-open intervals as a base.

Answer 1