Beriev's classification of distinct semicontinuous and monotone functions
1 Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
2 Jan Kokhanowski University, Kielce, 25-001, Poland
Keywords:
Beriev's classification, distinct semicontinuous and monotone functions
Abstract
We show that functions of two variables which are upper semi-continuous in the first variable and lower semi-continuous in the second variable, and functions which are monotonous in the first variable and continuous in the second variable belong to the first Baire class.
References
[1] Baire R. Sur les fonctions de variebles reeles // Analli di Mat. pura ed appl., ser 3.- 1899.- T.3- P.1-123.
[2] Mykhailiuk V.V. Beriev classification of pointwise discontinuous functions // Nauk. visn. Cherniv. u-tu. Vol. 76. Mathematics. - Chernivtsi: ChDU, 2000. - P. 77-79.
[3] Maslyuchenko V.K., Sobchuk O.V. Beriev classification and $σ$-metric spaces // Mat. studii. - 1994. - 3. - P. 95-101.
Cite
- ACS Style
- Mykhaylyuk, V. Beriev's classification of distinct semicontinuous and monotone functions. Bukovinian Mathematical Journal. 2018, 1
- AMA Style
- Mykhaylyuk V. Beriev's classification of distinct semicontinuous and monotone functions. Bukovinian Mathematical Journal. 2018; 1(349).
- Chicago/Turabian Style
- Volodymyr Mykhaylyuk. 2018. "Beriev's classification of distinct semicontinuous and monotone functions". Bukovinian Mathematical Journal. 1 no. 349.
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