Algebraically Determined Rings of Functions

Description:

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.

Creator(s): McLinden, Alexander Patrick
Creation Date: August 2010
Partner(s):
UNT Libraries
Collection(s):
UNT Theses and Dissertations
Usage:
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Creator (Author):
Publisher Info:
Publisher Name: University of North Texas
Place of Publication: Denton, Texas
Date(s):
  • Creation: August 2010
Description:

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.

Degree:
Level: Doctoral
Discipline: Mathematics
Physical Description:

iv, 47 p.

Language(s):
Subject(s):
Keyword(s): Polish Rings | descriptive set theory | algebraically determined
Contributor(s):
Partner:
UNT Libraries
Collection:
UNT Theses and Dissertations
Identifier:
  • OCLC: 711092491 |
  • UNTCAT: b3961966 |
  • ARK: ark:/67531/metadc31543
Resource Type: Thesis or Dissertation
Format: Text
Rights:
Access: Public
License: Copyright
Holder: McLinden, Alexander Patrick
Statement: Copyright is held by the author, unless otherwise noted. All rights reserved.