\mathcal{J}-approximately continuous functions

Abstract

In this paper density-like points and density-like topology connected with a sequence
$\mathcal{J} = \{J}_n n \in \mathbb{N}$ of closed intervals tending to $0$ will be considered. We will introduce the
notion of an $\mathcal{J}$-approximately continuous function associated with that kind of density
points. Moreover, we will present some properties of these functions and show their connection
with continuous functions with respect to such density topology.