Baire functions and non-isolated non-monotone discontinuities

Baire functions and non-isolated non-monotone discontinuities

We show that a Baire function on a metric space can be described in terms of its restrictions on specific subsets. Furthermore, it is proved that for a real-valued function on a subset of R, among all points of discontinuity, the non-isolated non-monotone points are crucial to determining whether th...

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Veröffentlicht in:Topology and its applications 2024-03, Vol.345, p.108842, Article 108842
Hauptverfasser: Veerapazham, Murugan, Antony, Kiran
Format: Artikel
Sprache:eng
Schlagworte:
Baire function
Borel of additive class k
Discontinuity
Non-monotone point
Perfect kernel
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Zusammenfassung:We show that a Baire function on a metric space can be described in terms of its restrictions on specific subsets. Furthermore, it is proved that for a real-valued function on a subset of R, among all points of discontinuity, the non-isolated non-monotone points are crucial to determining whether the function is a Baire function or not.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2024.108842