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You searched for subject:(topological uniqueness). Showing records 1 – 2 of 2 total matches.

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University of North Texas

1. Rees, Michael K. Topological uniqueness results for the special linear and other classical Lie Algebras.

Degree: 2001, University of North Texas

Suppose L is a complete separable metric topological group (ring, field, etc.). L is topologically unique if the Polish topology on L is uniquely determined by its underlying algebraic structure. More specifically, L is topologically unique if an algebraic isomorphism of L with any other complete separable metric topological group (ring, field, etc.) induces a topological isomorphism. A local field is a locally compact topological field with non-discrete topology. The only local fields (up to isomorphism) are the real, complex, and p-adic numbers, finite extensions of the p-adic numbers, and fields of formal power series over finite fields. We establish the topological uniqueness of the special linear Lie algebras over local fields other than the complex numbers (for which this result is not true) in the context of complete separable metric Lie rings. Along the way the topological uniqueness of all local fields other than the field of complex numbers is established, which is derived as a corollary to more general principles which can be applied to a larger class of topological fields. Lastly, also in the context of complete separable metric Lie rings, the topological uniqueness of the special linear Lie algebra over the real division algebra of quaternions, the special orthogonal Lie algebras, and the special unitary Lie algebras is proved. Advisors/Committee Members: Kallman, Robert, Brand, Neal.

Subjects/Keywords: Lie algebras.; Algebras, Linear.; Topological algebras.; Polish spaces (Mathematics); Lie algebra; Lie ring; topological uniqueness; pecial linear Lie algebra; polish space

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

APA (6th Edition):

Rees, M. K. (2001). Topological uniqueness results for the special linear and other classical Lie Algebras. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc3000/

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):

Rees, Michael K. “Topological uniqueness results for the special linear and other classical Lie Algebras.” 2001. Thesis, University of North Texas. Accessed July 14, 2020. https://digital.library.unt.edu/ark:/67531/metadc3000/.

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

MLA Handbook (7th Edition):

Rees, Michael K. “Topological uniqueness results for the special linear and other classical Lie Algebras.” 2001. Web. 14 Jul 2020.

Vancouver:

Rees MK. Topological uniqueness results for the special linear and other classical Lie Algebras. [Internet] [Thesis]. University of North Texas; 2001. [cited 2020 Jul 14]. Available from: https://digital.library.unt.edu/ark:/67531/metadc3000/.

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

Council of Science Editors:

Rees MK. Topological uniqueness results for the special linear and other classical Lie Algebras. [Thesis]. University of North Texas; 2001. Available from: https://digital.library.unt.edu/ark:/67531/metadc3000/

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


University of Florida

2. Neal, D. J ( David J ). Optional stochastic integration in Hilbert space with applications to nuclear spaces.

Degree: 1988, University of Florida

Subjects/Keywords: Hilbert spaces; Infinity; Martingales; Mathematics; Perceptron convergence procedure; Separable spaces; Stieltjes integral; Stopping distances; Topological theorems; Uniqueness; Hilbert space; Mathematics Thesis Ph.D; Nuclear spaces (Functional analysis); Stochastic integrals

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

APA (6th Edition):

Neal, D. J. (. D. J. ). (1988). Optional stochastic integration in Hilbert space with applications to nuclear spaces. (Thesis). University of Florida. Retrieved from https://ufdc.ufl.edu/AA00039502

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):

Neal, D J ( David J ). “Optional stochastic integration in Hilbert space with applications to nuclear spaces.” 1988. Thesis, University of Florida. Accessed July 14, 2020. https://ufdc.ufl.edu/AA00039502.

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

MLA Handbook (7th Edition):

Neal, D J ( David J ). “Optional stochastic integration in Hilbert space with applications to nuclear spaces.” 1988. Web. 14 Jul 2020.

Vancouver:

Neal DJ(DJ). Optional stochastic integration in Hilbert space with applications to nuclear spaces. [Internet] [Thesis]. University of Florida; 1988. [cited 2020 Jul 14]. Available from: https://ufdc.ufl.edu/AA00039502.

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

Council of Science Editors:

Neal DJ(DJ). Optional stochastic integration in Hilbert space with applications to nuclear spaces. [Thesis]. University of Florida; 1988. Available from: https://ufdc.ufl.edu/AA00039502

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

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