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ON TOTALLY BOUNDED AND COMPACT SETS IN THE SPACE OF CLOSED SUBSETS OF A METRIC SPACE

Annotation

The work continues the studies [1, 2] of the space clos(X) of non-empty closed subsets of a metric space X, the former being endowed with the metric ρ . In particular, the criteria of total boundedness and compactness of sets in (clos(X), ρ ) are considered.

Keywords

space of closed subsets of a metric space; totally bounded set; compact set

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UDC

515.124

Pages

1340-1344

References

1. Zhukovskiy E.S., Panasenko E.A. On multi-valued maps with images in the space of closed subsets of a metric space // Fixed Point Theory and Applications 2013, 2013:10 doi:10.1186/1687-1812-2013-10. 2. Zhukovskij E.S., Panasenko E.A. Opredelenie metriki prostranstva clos(X) zamknutyh podmnozhestv metricheskogo prostranstva X i svojstva otobrazhenij so znachenijami v clos (Rn) // Matematicheskij sbornik. 2014. T. 205. № 9. C. 65–96. 3. Zhukovskij E.S., Panasenko E.A. Ob odnoj metrike v prostranstve nepustyh zamknutyh podmnozhestv prostranstva Rn // Vestnik Udmurtskogo universiteta. Matematika. Mehanika. Komp'juternye nauki. 2012. Vyp. 1. C. 15–25. 4. Grigorenko A.A., Panasenko E.A. Asimptoticheskie svojstva mnozhestv reshenij differencial'nyh vkljuchenij. Tambov: Izdatel'skij dom TGU im. G.R. Derzhavina, 2009. 141 s. 5. Kolmogorov A.N., Fomin S.V. Jelementy teorii funkcij i funkcional'nogo analiza. M.: Nauka, 1976. 544 s.

Received

2015-04-15

Section of issue

Scientific articles

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