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University of North Texas

1. McLinden, Alexander Patrick. Algebraically Determined Rings of Functions.

Degree: 2010, University of North Texas

Let R be any of the following rings: the smooth functions on R2n 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. Advisors/Committee Members: Kallman, Robert R., UrbaƄski, Mariusz, Brozovic, Douglas.

Subjects/Keywords: Polish Rings; descriptive set theory; algebraically determined; Rings (Algebra); Functions.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

McLinden, A. P. (2010). Algebraically Determined Rings of Functions. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc31543/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

McLinden, Alexander Patrick. “Algebraically Determined Rings of Functions.” 2010. Thesis, University of North Texas. Accessed September 26, 2020. https://digital.library.unt.edu/ark:/67531/metadc31543/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

McLinden, Alexander Patrick. “Algebraically Determined Rings of Functions.” 2010. Web. 26 Sep 2020.

Vancouver:

McLinden AP. Algebraically Determined Rings of Functions. [Internet] [Thesis]. University of North Texas; 2010. [cited 2020 Sep 26]. Available from: https://digital.library.unt.edu/ark:/67531/metadc31543/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

McLinden AP. Algebraically Determined Rings of Functions. [Thesis]. University of North Texas; 2010. Available from: https://digital.library.unt.edu/ark:/67531/metadc31543/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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