Displaying similar documents to “F-limit points in dynamical systems defined on the interval”

Baire-one mappings contained in a usco map

Ondřej F. K. Kalenda (2007)

Commentationes Mathematicae Universitatis Carolinae

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We investigate Baire-one functions whose graph is contained in the graph of a usco mapping. We prove in particular that such a function defined on a metric space with values in ℝ d is the pointwise limit of a sequence of continuous functions with graphs contained in the graph of a common usco map.

The convergence space of minimal usco mappings

R. Anguelov, O. F. K. Kalenda (2009)

Czechoslovak Mathematical Journal

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A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to a uniform convergence structure so that the convergence space is complete. The important issue of the denseness of the...

Equiconnected spaces and Baire classification of separately continuous functions and their analogs

Olena Karlova, Volodymyr Maslyuchenko, Volodymyr Mykhaylyuk (2012)

Open Mathematics

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We investigate the Baire classification of mappings f: X × Y → Z, where X belongs to a wide class of spaces which includes all metrizable spaces, Y is a topological space, Z is an equiconnected space, which are continuous in the first variable. We show that for a dense set in X these mappings are functions of a Baire class α in the second variable.