Are you referring to Heath's paper "Screenability, pointwise paracompactness, .." in the CJM? He gives two arguments, the second referring to McAuley's paper. You don't like this one as well?
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.
I have Heath's paper. In the page 766, Heath gave this example of non screenable Moore space. He said that we can show that tangent V topology is not screenable follow readily by a category arguement or by another method I didn't understand it. If you can halp me in order to show that tangent V topology is not screenable by a simple way, I will be very gratefull to you.
Thank you in advance
Hello Mr. ojones
Certainly I know what is it mean by screenable space, otherwise how could I ask about it ? In short, a topological space is called screenable if for each open covering , there is a sequence of collections of pairwise disjoint open sets such that union of is a refinement of .
Thank you very much Mr. ojones. You gave me the arguement I shall use in order to prove that such a condition fails. That is by taking the set of V's whose vertex is irrationals and using the fact that irrationals are second category subset of the reals. Since this is the time of my final exam, I will complet the prove and write it properly at the end of my exams, and then I will write it here.
Thank you very very much Sir for your help and guidance.