Date of Graduation
Eberly College of Arts and Sciences
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.
Glatzer, Timothy James, "Continuities on Subspaces" (2013). Graduate Theses, Dissertations, and Problem Reports. 384.