Decomposable $n$-continuous mappings

In this paper, we introduce the concept of a decomposable $n$-continuous mapping, which is a generalization of the concept of a continuous mapping. We prove that decomposable $n$-continuous mappings preserve such topological invariants as the separability, the Lindelöf property, and the presence of a countable net. We also prove that a decomposable $n$-continuous mapping of a space with a countable base onto a compact Hausdorff space preserves the metrizability.