Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

You searched for +publisher:"University of Arizona" +contributor:("Suchanek, Amy"). One record found.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters


University of Arizona

1. Griesan, Raymond William. Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles.

Degree: 1988, University of Arizona

Metric topologies can be viewed as one-dimensional measures. This dissertation is a topological study of two-dimensional measures. Attention is focused on locally convex vector topologies on infinite dimensional real spaces. A nabla (referred to in the literature as a 2-norm) is the analogue of a norm which assigns areas to the parallelograms. Nablas are defined for the classical normed spaces and techniques are developed for defining nablas on arbitrary spaces. The work here brings out a strong connection with tensor and wedge products. Aside from the normable theory, it is shown that nabla topologies need not be metrizable or Mackey. A class of concretely given non-Mackey nablas on the ā„“p and Lp spaces is introduced and extensively analyzed. Among other results it is found that the topological dual of ā„“ā‚ with respect to these nabla topologies is Cā‚€, one of the spaces infamous for having no normed predual. Also, a connection is made with the theory of two-norm convergence (not to be confused with 2-norms). In addition to the hard analysis on the classical spaces, a duality framework from which to study the softer aspects is introduced. This theory is developed in analogy with polar duality. The ideas corresponding to barrelledness, quasi-barrelledness, equicontinuity and so on are developed. This dissertation concludes with a discussion of angles in arbitrary normed spaces and a list of open questions. Advisors/Committee Members: Lomont, John (advisor), Suchanek, Amy (committeemember), Wright, A. Larry (committeemember), Benson, Clark (committeemember), Laetsch, Theodore (committeemember).

Subjects/Keywords: Locally convex spaces.; Topological spaces.; Vector spaces.

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

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

APA (6th Edition):

Griesan, R. W. (1988). Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/184510

Chicago Manual of Style (16th Edition):

Griesan, Raymond William. “Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles. ” 1988. Doctoral Dissertation, University of Arizona. Accessed March 03, 2021. http://hdl.handle.net/10150/184510.

MLA Handbook (7th Edition):

Griesan, Raymond William. “Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles. ” 1988. Web. 03 Mar 2021.

Vancouver:

Griesan RW. Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles. [Internet] [Doctoral dissertation]. University of Arizona; 1988. [cited 2021 Mar 03]. Available from: http://hdl.handle.net/10150/184510.

Council of Science Editors:

Griesan RW. Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles. [Doctoral Dissertation]. University of Arizona; 1988. Available from: http://hdl.handle.net/10150/184510

.