Publication:
Algebraically Determined Rings of Functions
Algebraically Determined Rings of Functions
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Date
1900
Authors
McLinden, Alexander Patrick
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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.
Description
Publisher: University of North Texas ; Source: https://digital.library.unt.edu/ark:/67531/metadc31543/ ; Level: Thesis
Keywords
Polish Rings,
descriptive set theory,
algebraically determined,
Rings (Algebra),
Functions.