Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
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Application of adhesives to the Baire classification of maps of one variable.

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Published Apr 25, 2017
DOI https://doi.org/10.15673/tmgc.v9i3-4.317

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Olena Karlova
Yurii Fedkovych Chernivtsi National University

Abstract

We introduce a notion of (locally) weak adhesive space and consider some applications of weak adhesives to Baire classification of Lebesgue and fragmented maps.
Keywords:
weak adhesive space, Lebesgue-Hausdorff Theorem, Baire classification, fragmented map

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How to Cite
Karlova, O. (2017). Application of adhesives to the Baire classification of maps of one variable. Proceedings of the International Geometry Center, 9(3-4). https://doi.org/10.15673/tmgc.v9i3-4.317
Issue
Vol 9 No 3-4 (2016)
Section
Papers

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References

1. R. Baire. Sur les fonctions de variables re´elles. Ann. Mat. Pura Appl., 3(3):1–123, 1899.

2. S. Banach. ¨Uber analytisch darstellbare operationen in abstrakten r¨aumen. Fund. Math., 17(1):283–295, 1931.

3. K. Borsuk. Theory of retracts. PWN - Polish Scientific Publisher, 1967.

4. R. Engelking. General Topology. Heldermann Verlag, Berlin, 1989.

5. M. Fosgerau. When are Borel functions Baire functions? Fund. Math., 143, 1993.

6. R.W. Hansell. Borel measurable mappings for nonseparable metric spaces. Trans. Amer. Math. Soc., 161:145–169, 1971.

7. R.W. Hansell. On Borel mappings and Baire functions. Trans. Amer. Math. Soc., 194:195–211, 1974.

8. F. Hausdorff. Set Theory. Amer. Math. Soc., 1957.

9. O. Karlova. Functionally -discrete mappings and a generalization of Banach’s theorem. Top. Appl., 189, 2015.

10. O. Karlova. On Baire classification of mappings with values in connected spaces. Eur. J. Math., 2(2):526–538, 2016.

11. O. Karlova. On Baire-one mappings with zero-dimensional domains. Colloq. Math., 147(1):129–142, 2017.

12. O. Karlova, V. Mykhaylyuk. On stable Baire classes. Acta Math. Hungar., 150(1):36–48, 2016.

13. O. Karlova, V. Mykhaylyuk. On composition of Baire functions. Top. Appl., 216, 2017.

14. G. Koumoullis. A generalization of functions of the first class. Top. Appl., 50, 1993.

15. H. Lebesgue. Sur l’approximation des fonctions. Bull. Sci. Math., 22, 1898.

16. K. Morita. Paracompactness and product spaces. Fund. Math., 50, 1962.

17. S. Rolewicz. On inversion of non-linear transformations. Studia Math., 17, 1958.

18. C. Stegall. Functins of the first baire class with values in banach spaces. Proc. Amer. Math. Soc., 111, 1991.

19. L. Vesel´y. Characterization of Baire-one functions between topological spaces. Acta Univ. Carol., Math. Phys., 33(2):143–156, 1992.