Equi-Baire 1 families of functions

Ascoli-Type Theorem for Baire 1 Functions

“…The theory developed in this paper could be of interest to mathematicians working in fields including topology [13], functional analysis [10], and dynamical systems [11,12].…”

“…It is known that if Y = R, the Baire 1 function is a limit of a pointwise convergent sequence of continuous functions. There is rich literature concerning Baire 1 functions; see [8][9][10][11][12][13][14] and others.…”

“…In our paper, we prove Ascoli-type theorem for locally bounded Baire 1 functions using a special form of equi-Lebesgue family. The notion of equi-Lebesgue family of functions from X to Y was introduced in [14], and it also appeared in [10] and in [11]. If X is a separable metric space, then the notion of equi-Lebesgue family coincides with the notion of equi-Baire 1 family introduced by Lecomte in his paper [10].…”

Baire 1 Functions and the Topology of Uniform Convergence on Compacta

“…(cf. (p. 375, [6]), [7]) Let X and Y be metric spaces. For f : X → Y, consider the following conditions:…”

“…Proof. (7) ⇒ (1) Let {K n : n ∈ N} be a countable cofinal subfamily in K(X) with respect to the inclusion. The family {W(K, ε) :…”