On dynamics of families of equi-Baire one functions on metric spaces

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].…”

“…Notice that the notion of equi-Baire 1 family of functions can also be found in the paper of Alighani-Koopaei [11], who showed its applications in 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.…”

Equi-Baire 1 families of functions

“…The characterization of Baire 1 functions by LTZ-property motivated Lecomte in his paper [15] to introduce the notion of equi-Baire 1 family of functions. Then it was rediscovered by Alighani-Koopaei [1] who showed its applications in dynamical systems; see also his recent paper [2]. Definition 3.1.…”

“…(2) ⇒ (1): By (2) consider a subsequence (f n k ) of (f n ) described in (2). By Theorem 5.2 there is a subsequence of the sequence (f n k ) which uniformly converges on X.…”