Some unpublished Reclaw theorems and their applications to Baire-star-one functions

Authors

TOMASZ NATKANIEC
WALDEMAR SIEG

Abstract

Lunina's 7-tuples $\langle E^1,\ldots, E^7\rangle$ of sets of pointwise convergence, divergence to $\infty$, divergence to $-\infty$, etc. for sequences of Baire-star-one functions are cha\-racterized. Generalization on ideal convergence of such sequences is discussed. Limits and ideal limits of sequences of Baire-star-one functions are considered in the last part of the article.

DOI

10.3906/mat-1811-103

Keywords

Pointwise convergence, ideal convergence, $F_\sigma$-ideal, $\cI^\star$-universal set, $\omega$-diagonalizability, Lunina 7-tuples, Baire-one-star functions

First Page

1148

Last Page

1160

Recommended Citation

NATKANIEC, TOMASZ and SIEG, WALDEMAR (2019) "Some unpublished Reclaw theorems and their applications to Baire-star-one functions," Turkish Journal of Mathematics: Vol. 43: No. 3, Article 7. https://doi.org/10.3906/mat-1811-103
Available at: https://journals.tubitak.gov.tr/math/vol43/iss3/7