Let collection of subsets of =2 : {(a, b) × {c}| a, b & c2= and a < b}. This is collection of all horizontal intervals.
Illustrate that Horizontal Interval Topology and Vertical Interval Topology are not comparable. Determine the set which is open in Horizontal Interval Topology and not in Vertical Interval Topology and then compute the set which is open in Vertical Interval Topology and not in Horizontal Interval Topology.