Semester
Fall
Date of Graduation
2013
Document Type
Dissertation
Degree Type
PhD
College
Eberly College of Arts and Sciences
Department
Mathematics
Committee Chair
Krzysztof Ciesielski
Committee Co-Chair
Edgar Fuller
Committee Member
John Goldwasser
Committee Member
Robert Mnatsakanov
Committee Member
Jerzy Wojciechowski
Abstract
We 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.
Recommended Citation
Glatzer, Timothy James, "Continuities on Subspaces" (2013). Graduate Theses, Dissertations, and Problem Reports. 384.
https://researchrepository.wvu.edu/etd/384