Decomposable n-Continuous Mappings

Abstract

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.