Newsgroups: sci.math
From: kwhyte@hog.uchicago.edu (Kevin Whyte)
Subject: Non-paracompact manifolds
Date: Wed, 1 Apr 1992 06:04:49 GMT
Let me give some motivation, since the question I want
to ask is very vague. I recently ran in to the long line
again, after almost forgetting about it since point-set
topology. It is a non-paracompact manifold with some strange
properies ( The tangent bundle is non-trivial, it has inf.
many distinct analytic structures, etc.).
Brief review of the long line:
First, the idea is to stick uncountably many copies of [0,1)
end to end. The real line is countably many, i.e. take the
set [0,1) x N with the topology coming from the dictionary
ordering. This is just [0,inf) in the obvious way. To do
the same thing uncountably many times, take S to be the minimal,
uncountable, well-ordered set (minimal meaning for all s in S
the set of t