Date of Award
1993
Document Type
Thesis
Publication Status
Version of Record
Submission Date
October 2026
Thesis/Dissertation Advisor [Chair]
Schaefer, Helmut H.
Abstract
The general properties of sequentially continuous linear forms are studied with the aid of two topologies derived from an original topology. The first of these is the finest topology which preserves sequential convergence relative to the given topology, and the second is obtained by limiting consideration to locally convex ground spaces. The latter topology displays unexpected permanence properties, allowing the development of a sequential analogue to the standard theory of topological vector spaces. A natural application of the theory is to locally convex spaces for which sequential and full continuity are equivalent. This property is enjoyed by bornological spaces, however it is not sufficient to characterize them. A new class of locally convex spaces is introduced, which is defined by this condition and shown to be a strict generalization of bornological spaces. The properties of this new class and its variants are explored and a striking example of a non-bornological space belonging to the class is obtained by the Riesz Representation Theorem.
Extent
119 p.
Recommended Citation
Beatty, Thomas, "Sequential topologies and their application to a new class of locally convex spaces" (1993). Electronic Theses and Dissertations 1990 - 1999. 501.
https://digitalcommons.fau.edu/etd_general_4/501
Identifier
FADT12337
Comments
Thesis (Ph.D.)--Florida Atlantic University, 1993.|Thesis (Ph.D.)--Florida Atlantic University, 1993.