On some cardinal invariants of hyperspaces

R.B.Beshimov

We investigate relationships between some cardinal invariants of a $T_1$-space $X$ and its hyperspace $\exp(X)$ of all non-empty closed subsets of $X$, endowed with the Vietoris topology. We shall prove that hyperspace construction $\exp$ preserves $\pi$-weight and calibers. We compare $\pi$-characters of various hyperspace constructions: $\exp_n$, $\exp_\omega$, $\exp_c$, $\exp$.

1. Архангельский А.В., Пономарев В.И. О диадических бикомпактах, ДАН СССР 182 (1968), № 5, 993-996.

2. Engelking R. General Topology, Heldermann Verlag, Berlin, 1989.

3. Федорчук В.В., Филиппов В.В. Общая топология. Основные конструкции.-- М.: МГУ, 1988.-- 252~с.

4. Fedorchuk V.V., Todorcevic S. Cellularity of covariant functors. Topology and its Appl., 76 (1997), 125-150.

5. Jech T.J. Lectures in Set-Theory with Particular Emphasis on the Method of Forcing. Berlin. 1971.

6. Шанин Н.А. О произведении топологических пространств, Труды Мат. Инст. им. В. А. Стеклова АН СССР, 24 (1948), 1--112.

7. Todorcevic S. Remarks on cellularity in products. Compositio Math., 57 (1986), 357-372.

	On some cardinal invariants of hyperspaces
Author	R.B.Beshimov mathinst@uzsci.net Department of Algebra and Analysis, V. I. Romanovsky Institute of Mathematics, Uzbek Academy of Sciences,
Abstract	We investigate relationships between some cardinal invariants of a $T_1$-space $X$ and its hyperspace $\exp(X)$ of all non-empty closed subsets of $X$, endowed with the Vietoris topology. We shall prove that hyperspace construction $\exp$ preserves $\pi$-weight and calibers. We compare $\pi$-characters of various hyperspace constructions: $\exp_n$, $\exp_\omega$, $\exp_c$, $\exp$.
Keywords	cardinal invariant, hyperspace, Vietoris topology
DOI	doi:10.30970/ms.24.2.197-202
Reference	1. Архангельский А.В., Пономарев В.И. О диадических бикомпактах, ДАН СССР 182 (1968), № 5, 993-996. 2. Engelking R. General Topology, Heldermann Verlag, Berlin, 1989. 3. Федорчук В.В., Филиппов В.В. Общая топология. Основные конструкции.-- М.: МГУ, 1988.-- 252~с. 4. Fedorchuk V.V., Todorcevic S. Cellularity of covariant functors. Topology and its Appl., 76 (1997), 125-150. 5. Jech T.J. Lectures in Set-Theory with Particular Emphasis on the Method of Forcing. Berlin. 1971. 6. Шанин Н.А. О произведении топологических пространств, Труды Мат. Инст. им. В. А. Стеклова АН СССР, 24 (1948), 1--112. 7. Todorcevic S. Remarks on cellularity in products. Compositio Math., 57 (1986), 357-372.
Pages	197-202
Volume	24
Issue	2
Year	2005
Journal	Matematychni Studii
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