Which surfaces can be completely defined by a single parameterization? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T12:52:40Z http://mathoverflow.net/feeds/question/120733 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/120733/which-surfaces-can-be-completely-defined-by-a-single-parameterization Which surfaces can be completely defined by a single parameterization? pritam 2013-02-04T06:46:05Z 2013-02-04T07:09:49Z <p>It can be easily shown that any closed and bounded surface of \$\mathbb{R}^3\$ cannot be covered by a single surface patch, i.e. cannot be homeomorphic to an open set of \$\mathbb{R}^2\$. What can be said about the non-compact surfaces? Is it possible to characterize all the surfaces of \$\mathbb{R}^3\$ which are homeomorphic to an open set of \$\mathbb{R}^2\$?</p>