Separate continuity topology and a generalization of Sierpinski's theorem (in Ukrainian) |
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| Author |
Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, Ukraine
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| Abstract |
The separate continuity topology is considered and some its properties are investigated. With help of these properties a generalization of Sierpinski theorem on determination of a real separately continuous function by its values on a dense set is obtained.
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| Keywords |
separate continuity topology, properties of separate continuity, Sierpinski theorem, determination by dense set, real functions, generalization of Sierpinski theorem
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| DOI |
doi:10.30970/ms.14.2.193-196
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Reference |
1. Sierpiński W. Sur une propertie de fonctions de deux variables réeles, continues par rapport à chacune de variables // Publ. Math. Univ. Belgrade. – 1932. – V.1. – P.125–128.
2. Piotrowski Z., Wingler E.Y. On Sierpiński's theorem on the determination of separately continuous functions // Q$\&$A in General Topology.\ -- 1997.\ -- V. 15.\ -- 1997.\ -- P.15--19. 3. Piotrowski Z. Quasi-continuity and product spaces // Proc. Intern. Geom. Top., Warshawa. – 1980. – P.349–352. |
| Pages |
193-196
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| Volume |
14
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| Issue |
2
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| Year |
2000
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| Journal |
Matematychni Studii
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