Collections of compact sets and functions having \(G_\delta\)-graphs. (English) Zbl 1134.26001

Jordan, Francis

Real Anal. Exch. 32(2006-2007), No. 2, 287-302 (2007).

The author investigates the connection between the structure of a function \(f\) defined on a subset of a space \(X\) and the Borel complexity of the set \(C(f)= \{C\in J(x): f|_C\) is continuous}, where \(I(X)\) denotes the nonempty compact subsets of \(X\) with the Hausdorff metric. Two hierarchies of functions with \(G_\delta\)-graphs are also defined.

Reviewer: Zoltán Finta (Cluj-Napoca)

MSC:

26A15	Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
03E15	Descriptive set theory

Keywords:

Borel complexity; continuous functions