Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
Math Topics
»
geometry.research
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
Classification of 1manifolds (was: 1manifold homeomeorphic to R)
Replies:
7
Last Post:
May 3, 2009 5:50 AM




Classification of 1manifolds (was: 1manifold homeomeorphic to R)
Posted:
Apr 19, 2009 9:31 AM


Rodolfo Medina <rodolfo.medina@gmail.com> writes:
> Here: > > [...] > > http://en.wikipedia.org/wiki/Topological_manifold > > , `Classification of manifolds', it is stated that a connected 1topological > manifold is homeomorphic to R.
Alfredo Restrepo Palacios <arestrep@uniandes.edu.co> writes:
> Hi,up to homeomorphisms, there are only two connected (separable, metric) > 1manifolds: the (noncompact) open interval I' and the (compact) circle > S1. They are both orientable, the "real projective line" is also S1. You can > also take a look at Christenson and Voxman, Aspects of Topology,
Thanks. I haven't looked at the book you suggest yet. But here:
http://en.wikipedia.org/wiki/Long_line_(topology)
it is stared a more general result: that a 1manifolds with boundary is homeomorphic either to R or to the circle, or even to a closed or halfopen R interval.
Can anybody suggest where to find a complete demonstration of this more general statement? Or maybe the demonstration reported by Prof. Lee can be easily generalized?
Thanks for any help Rodolfo



