First Baire class functions in the pluri-fine topology
Oleksiy Dovgoshey, Mehmet K\"u\c{c}\"ukaslan, Juhani Riihentaus

TL;DR
This paper establishes the equivalence of two classes of first Baire class functions in the pluri-fine topology on complex domains and shows these functions can be represented as diagonals of separately continuous functions.
Contribution
It proves the equality of the first Baire class and the first functional Lebesgue class in the pluri-fine topology and characterizes these functions as diagonals of separately continuous functions.
Findings
Proves $B_{1}(\Omega, \\mathbb R) = H_{1}^{*}(\Omega, \\mathbb R)$.
Shows each first Baire class function is a diagonal of a separately continuous function.
Establishes a link between Baire class functions and separately continuous functions in the pluri-fine topology.
Abstract
Let be the first Baire class of real functions in the pluri-fine topology on an open set and let be the first functional Lebesgue class of real functions in the same topology. We prove the equality and show that for every there is a separately continuous function in the pluri-fine topology on such that is the diagonal of
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Topology and Set Theory
