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Matematicheskie Zametki, 2013, Volume 93, Issue 3, Pages 368–372
DOI: https://doi.org/10.4213/mzm8833 (Mi mzm8833) 		 
Maps to Spaces of Compacta Determined by Limit Sets

A. P. Devyatkov

Tyumen State University
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DOI: https://doi.org/10.4213/mzm8833
Abstract: For a sequence of functions on the unit disk $D\subset\mathbb C$, the map of the boundary circle to a space of compact sets with Hausdorff metric which takes each point $e^{i\theta}\in\partial D$ to the limit set of the sequence of functions at this point is considered. It is shown that such a map is of Borel class at most 4.
Keywords: Borel map, Borel class, limit set of a sequence of functions, Hausdorff metric.
Received: 15.03.2010
Revised: 16.03.2012
English version:
Mathematical Notes, 2013, Volume 93, Issue 3, Pages 392–396
DOI: https://doi.org/10.1134/S000143461303005X
Bibliographic databases:
Document Type: Article
UDC: 517.544.72
Language: Russian
Citation: A. P. Devyatkov, “Maps to Spaces of Compacta Determined by Limit Sets”, Mat. Zametki, 93:3 (2013), 368–372; Math. Notes, 93:3 (2013), 392–396
Citation in format AMSBIB
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