Hello all mathematicians:

If is the upper half plane including the real axis , we let each point above the real axis be open and take as a neighborhood basis of points a "V" with vertex at , sides of slopes ±1 and height . I showed that is a metacompact Moore space. But I need your help in order to show that is not screenable. I found in Heath's paper that is not screenable follow directly by a category arguement. But I don't catch the idea honestly. This topological space is called the tangent V topology.

Please guide me and every advise is highly appreciated.