Fiibrations property of embedding maps of orbifold charts

In this paper we introduce the notion of Hurewicz fibrations in the class of embedding maps of orbifold charts by giving the concept of E-fibration embedding. We study the fundamental properties of this concept such as the restriction, product and its relationship with Hurewicz fibration, etc. Furthermore, we introduce the notion of lifting functions of E-fibration embedding and study preserving projection property of these lifting functions.