Let R be any of the following rings: the smooth functions on R^2n with the Poisson bracket, the Hamiltonian vector fields on a symplectic manifold, the Lie algebra of smooth complex vector fields on C, or a variety of rings of functions (real or complex valued) over 2nd countable spaces. Then if H is any other Polish ring and φ:H →R is an algebraic isomorphism, then it is also a topological isomorphism (i.e. a homeomorphism). Moreover, many such isomorphisms between function rings induce a homeomorphism of the underlying spaces. It is also shown that there is no topology in which the ring of real analytic functions on R is a Polish ring.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc31543 |
| Date | 08 1900 |
| Creators | McLinden, Alexander Patrick |
| Contributors | Kallman, Robert R., Urbański, Mariusz, Brozovic, Douglas |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iv, 47 p., Text |
| Rights | Public, Copyright, McLinden, Alexander Patrick, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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