there exists a lifting (α ) ̃ ∶ (I,0) → (X̃,x̃0) of ???? such that p∘ α ̃= α. Also, the map p has unique path lifting property if for every path ???? in X, there is at most one lifting (α ) ̃ ∶ (I,0) → (X̃,x̃0) of ????. Recently, Brazas extend the concept of covering map to semicovering map. Kowkabi, Mashayekhy and torabi proved that, a semicovering map is a local homeomorphism with unique path lifting and path lifting properties. Since every covering or semicovering map ????∶ X ̃→???? has homotopy lifting property, every path ???? in ????̃ such that [p∘α] = 1 i.e. p∘α is null, ???? is a null homotopic loop. This fact motivated us to explore the (G,H)-covering map and (G,H)-semicovering map. In this paper, we introduce the (G,H)-covering map and (G,H)-semicovering map. We note that a (G,H)-covering map is a covering map, so it has the path lifting property, the unique path lifting, the homotopy lifting property and etc.. Also we investigate the properties of (G,H)-covering map and (G,H)-semicovering map. For example, if p∶(X̃,x̃0)→(X,x0) is a (G,H)-covering map or (G,H)-semicovering map and ???? is a path in ????̃ with α(0)=x̃0 and α (1)=x̃, then p∶(X̃,x̃0)→(X,x0) is a (α^(-1) Gα,(p∘α)^(-1) H(p∘α))-covering map or (α^(-1) Gα,(p∘α)^(-1) H(p∘α))-semicovering map.

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