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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 4, Pages 778–784
(Mi smj2124)
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This article is cited in 3 scientific papers (total in 3 papers)
The Katětov property for finite degree seminormal functors
A. V. Ivanov Petrozavodsk State University, Petrozavodsk, Russia
Abstract:
A seminormal functor $\mathscr F$ enjoys the Katětov property ($K$-property) if for every compact set $X$ the hereditary normality of $\mathscr F(X)$ implies the metrizability of $X$. We prove that every seminormal functor of finite degree $n>3$ enjoys the $K$-property. On assuming the continuum hypothesis ($CH$) we characterize the weight preserving seminormal functors with the $K$-property. We also prove that the nonmetrizable compact set constructed in [1] on assuming $CH$ is a universal counterexample for the $K$-property in the class of weight preserving seminormal functors.
Keywords:
seminormal functor, hereditary normality, Katětov cube theorem, Katětov property.
Received: 12.02.2008
Citation:
A. V. Ivanov, “The Katětov property for finite degree seminormal functors”, Sibirsk. Mat. Zh., 51:4 (2010), 778–784; Siberian Math. J., 51:4 (2010), 616–620
Linking options:
https://www.mathnet.ru/eng/smj2124 https://www.mathnet.ru/eng/smj/v51/i4/p778
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Abstract page: | 252 | Full-text PDF : | 80 | References: | 42 | First page: | 1 |
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