\(ls\)-Ponomarev-systems and 1-sequence-covering mappings

Abstract

In this paper, we prove that \(f\) is an l-sequence-covering (resp., 2-sequence-covering) mapping from a locally separable metric space \(M\) onto a space \(X\) if and only if \(\{(X_\lambda, \{P_{\lambda,n}\}): \lambda \in \Lambda\}\) is a double point-star \(wsn\)-cover (resp., double point-star \(sc\)-cover) for \(X\), where \((f, M, X, \{P_{\lambda,n}\})\) is an \(ls\)-Pomomarev-system, and investigate further properties of mappings in the  \(ls\)-Pomomarev-system \(f, M, X, \{P_{\lambda,n}\}\).