On the extension of real-valued continuous functions
1 Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
2 Jan Kokhanowski University, Kielce, 25-001, Poland
Keywords:
real-valued continuous functions
Abstract
Necessary and sufficient conditions for the extendibility of bounded continuous function to the Baire-one function are established. The extendibility of functions defined on $z$ -embedded sets of topological spaces is investigated.
References
[1] Kalenda, O., Spurný , J. Extending Baire-one functions on topological spaces // Topol. Appl. 149 (2005), 195 - 216.
[2] Lukeš J., Malý J., Zajíček. Fine topology methods in real analysis and potential theory, Lecture Notes in Math. 1189, Springer-Verlag. - 1986.
[3] Engelking R. General topology - M. Mir, 1986. - 752 p.
[4] Blair R., Hager A. Extension of zero-sets and of real-valued functions // Math. Z. - 136 . - 1974. - P. 41-52.
Cite
- ACS Style
- Karlova, O. On the extension of real-valued continuous functions. Bukovinian Mathematical Journal. 2018, 1
- AMA Style
- Karlova O. On the extension of real-valued continuous functions. Bukovinian Mathematical Journal. 2018; 1(454).
- Chicago/Turabian Style
- Olena Karlova. 2018. "On the extension of real-valued continuous functions". Bukovinian Mathematical Journal. 1 no. 454.
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