Abstract
dc:description.abstractWe define a generalized continuity by declaring that for any family S of subsets of a topological space X, a function f : X → Y is S -continuous if for each S∈ S , the function f ↾ S : S → Y is continuous. This is easily seen to generalize such well known concepts as separate continuity and linear continuity. Using this definition as a way to unify several disparate results, we attempt to create a theory of S -continuity. As a part of this program, we give constructions for S -continuous functions for several natural classes S , describe the sets of discontinuities of such functions (characterizing several classes), and discuss the regularity of such functions.
Degree
thesis:*- Name thesis:degree_name
- PhD
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Year dc:date.available
- 2013
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Glatzer, Timothy James
- Contributors dc:contributor
-
- Krzysztof Ciesielski
- Edgar Fuller
- John Goldwasser
- Robert Mnatsakanov
- Jerzy Wojciechowski
Subjects
dc:subject × 1Identifiers
dc:identifier.*- Identifier
- https://researchrepository.wvu.edu/etd/384
- OAI identifier oai:identifier
- oai:researchrepository.wvu.edu:etd-1387