On $\mathcal {P}$-scattered spaces (in Ukrainian)

B. Bokalo

The properties of $\mathcal {P}$-scattered spaces where $\mathcal {P}$ is the property of separability ($\S$-scattered) and metrizability ($\mathcal {M}$-scattered) are investigated. A characterization of compacta lying in a $\sigma$-product of metrizable compacta is given. In particular, it is shown that $\S$-scattered Eberlein compacta are Korson compacta. It is shown that, under some restrictions, the compactum which is a finite union of its $\mathcal {M}$-scattered subspaces is an Eberlein compactum.

1. Архангельский А.В. Топологические пространства функций.– М.: МГУ, 1989.

2. Архангельский А.В. Строение и классификация топологических пространств и кардинальные инварианты // УМН. 1978. Т.33, вып.6. С.29-84.

3. Бокало Б.М. Про деякi властивост1pt-1pt i дотикання тополог1pt-1pt iй розрiджених просторiв // Вiсник Львiв. ун-ту. 1989, вип.32. С.65-67.

4. Чобан М.М., Додон Н.К. Теория $\mathcal {P}$-разреженных пространств. Кишинев: Штиинца, 1979.

5. Энгелькинг Р. Общая топология. М.: Мир, 1986.

6. Alster K. Some remarks on Eberlein compacte // Fund. Math. 1979. V.104, N.1. P.43-46.

7. Gruenhage G. Covering properties on $X^2 \backslash \Delta , \; w$-sets, and compact subsets of $\Sigma $-products // Topol. and Appl. 1984. V.17, N.3. P.287-304.

8. Michael E., Rudin M.E. Another note on Eberlein compacts // Pacif. J. Math. 1977. V.72, N.2. P.497-499.

9. Nachmanson L.V., Yakovlev N.N. On compact sets lying in $\sigma$-products // Convent. Math. Univ. Carolinae. 1981. V.22. P.247-261. Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine

	On $\mathcal {P}$-scattered spaces (in Ukrainian)
Author	B. Bokalo Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine
Abstract	The properties of $\mathcal {P}$-scattered spaces where $\mathcal {P}$ is the property of separability ($\S$-scattered) and metrizability ($\mathcal {M}$-scattered) are investigated. A characterization of compacta lying in a $\sigma$-product of metrizable compacta is given. In particular, it is shown that $\S$-scattered Eberlein compacta are Korson compacta. It is shown that, under some restrictions, the compactum which is a finite union of its $\mathcal {M}$-scattered subspaces is an Eberlein compactum.
Keywords	P-scattered spaces, separability, §-scattered, metrizability, M-scattered, Eberlein compacta, Korson compacta
DOI	doi:10.30970/ms.2.1.73-77
Reference	1. Архангельский А.В. Топологические пространства функций.– М.: МГУ, 1989. 2. Архангельский А.В. Строение и классификация топологических пространств и кардинальные инварианты // УМН. 1978. Т.33, вып.6. С.29-84. 3. Бокало Б.М. Про деякi властивост1pt-1pt i дотикання тополог1pt-1pt iй розрiджених просторiв // Вiсник Львiв. ун-ту. 1989, вип.32. С.65-67. 4. Чобан М.М., Додон Н.К. Теория $\mathcal {P}$-разреженных пространств. Кишинев: Штиинца, 1979. 5. Энгелькинг Р. Общая топология. М.: Мир, 1986. 6. Alster K. Some remarks on Eberlein compacte // Fund. Math. 1979. V.104, N.1. P.43-46. 7. Gruenhage G. Covering properties on $X^2 \backslash \Delta , \; w$-sets, and compact subsets of $\Sigma $-products // Topol. and Appl. 1984. V.17, N.3. P.287-304. 8. Michael E., Rudin M.E. Another note on Eberlein compacts // Pacif. J. Math. 1977. V.72, N.2. P.497-499. 9. Nachmanson L.V., Yakovlev N.N. On compact sets lying in $\sigma$-products // Convent. Math. Univ. Carolinae. 1981. V.22. P.247-261. Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine
Pages	73-77
Volume	2
Issue	1
Year	1993
Journal	Matematychni Studii
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