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- W2248370642 abstract "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." @default.
- W2248370642 created "2016-06-24" @default.
- W2248370642 creator A5039736003 @default.
- W2248370642 date "2010-08-01" @default.
- W2248370642 modified "2023-10-16" @default.
- W2248370642 title "Algebraically Determined Rings of Functions" @default.
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