Some properties of $PP$-spaces

Karlova Olena; Sobchuk Oleksandr Vasyliovych

Karlova Olena ^1,2 , Sobchuk Oleksandr Vasyliovych ³

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

² Jan Kokhanowski University, Kielce, 25-001, Poland

³ Professional College of Yuriy Fedkovych Chernivtsi National University, Chernivtsi , 58000, Ukraine

Keywords: PP-spaces

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Abstract

It is obtained that the class of $PP$-spaces is closed under countable products. Besides it is proved that a compact $PP$-space is separable and a countable compact Hausdorff or a pseudo-compact $PP$-space is metrizable.

References

[1] Lebesgue H. Sur l`aproximation des fonctions // Bull. Sci. Math. - 1898. - 22 . - P. 278-287.

[2] Rudin W. Lebesgue first theorem // Math. Analysis and Applications, Part B. Edited by Nachbin. Adv. in Math. Supplem.Studies 78. - Academic Press, 1981. - P.741-747.

[3] Sobchuk O. $PP$-spaces and Baire classification // International Conference on Functional Analysis and its Applications, dedicated to the 110th anniversary of Stefan Banach. Book of abstracts (May 28-31, 2002). - Lviv, 2002. - P. 189.

[4] Sobchuk O.V. Beriev classification and Lebesgue spaces // Nauk. visn. Chernivtsi un-tu. - 2001. - vol. 111. - P. 110-113.

[5] Engelking R. General topology. - M.: Mir, 1986. -752 p.

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ACS Style: Karlova, O.; Sobchuk, O.V. Some properties of $PP$-spaces. Bukovinian Mathematical Journal. 2018, 1
AMA Style: Karlova O, Sobchuk OV. Some properties of $PP$-spaces. Bukovinian Mathematical Journal. 2018; 1(269).
Chicago/Turabian Style: Olena Karlova, Oleksandr Vasyliovych Sobchuk. 2018. "Some properties of $PP$-spaces". Bukovinian Mathematical Journal. 1 no. 269.

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