Displaying similar documents to “Equiconnected spaces and Baire classification of separately continuous functions and their analogs”

F-limit points in dynamical systems defined on the interval

Piotr Szuca (2013)

Open Mathematics

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Given a free ultrafilter p on ℕ we say that x ∈ [0, 1] is the p-limit point of a sequence (x n)n∈ℕ ⊂ [0, 1] (in symbols, x = p -limn∈ℕ x n) if for every neighbourhood V of x, {n ∈ ℕ: x n ∈ V} ∈ p. For a function f: [0, 1] → [0, 1] the function f p: [0, 1] → [0, 1] is defined by f p(x) = p -limn∈ℕ f n(x) for each x ∈ [0, 1]. This map is rarely continuous. In this note we study properties which are equivalent to the continuity of f p. For a filter F we also define the ω F-limit set of...

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.