Hello all mathematicians:

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

Please guide me and every advise is highly appreciated.