Algebraically Determined Rings of Functions Page: 2
iv, 47 p.View a full description of this dissertation.
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McLinden, Alexander Patrick. Algebraically Determined Rings of Functions. Doctor
of Philosophy (Mathematics), August 2010, 47 pp., bibliography, 15 titles.
Let R be any of the following rings: the smooth functions on R2T 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 <p: 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.
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McLinden, Alexander Patrick. Algebraically Determined Rings of Functions, dissertation, August 2010; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc31543/m1/2/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .