A new approach to proving Baire’s theorem on semi-continuous functions and one characterization of Beerness

Maslyuchenko Volodymyr Kyrylovych; Maslyuchenko Oleksandr Volodymyrovych; Fotiy Olena Georgiivna

Maslyuchenko Volodymyr Kyrylovych ¹ , Maslyuchenko Oleksandr Volodymyrovych ^2,1 , Fotiy Olena Georgiivna ¹

¹ Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

² Institute of Mathematics, University of Silesia in Katowice, Katowice, 40-007, Poland

Keywords: Baire’s theorem, semi-continuous functions, topological space

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Abstract

We provide a new proof of Baire’s theorem on semi-continuous functions and show that, a topological space $X$ is Baire if and only if every function $f : X → \mathbb{R}$ is almost cliquish.

References

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[5] Kuratovsky K. Topology. -T.1.- M.: Mir,1966. - 596 p.

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ACS Style: Maslyuchenko, V.K.; Maslyuchenko, O.V.; Fotiy, O.G. A new approach to proving Baire’s theorem on semi-continuous functions and one characterization of Beerness. Bukovinian Mathematical Journal. 2016, 3
AMA Style: Maslyuchenko VK, Maslyuchenko OV, Fotiy OG. A new approach to proving Baire’s theorem on semi-continuous functions and one characterization of Beerness. Bukovinian Mathematical Journal. 2016; 3(1).
Chicago/Turabian Style: Volodymyr Kyrylovych Maslyuchenko, Oleksandr Volodymyrovych Maslyuchenko, Olena Georgiivna Fotiy. 2016. "A new approach to proving Baire’s theorem on semi-continuous functions and one characterization of Beerness". Bukovinian Mathematical Journal. 3 no. 1.

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