Closed mappings, boundary-compact mappings and sequence-covering mappings (Q2834141)

Some results on generalized metric spaces are obtained. The basic ones may be stated as follows.NEWLINENEWLINETheorem 1. Suppose that \(X\) is a \(k^*\)-metrizable \(k\)-space and \(Y\) contains no copy of \(S_{\omega_1}\). Then, each \(f:X\to Y\) is a boundary-s-mapping.NEWLINENEWLINETheorem 2. Suppose that \(X\) is first countable and \(f:X\to Y\) is a sequence-covering boundary-Lindelöf mapping. Then, \(Y\) is snf-countable iff \(f\) is 1-sequence-covering.NEWLINENEWLINETheorem 3. Suppose that \(X\) is first-countable and \(f:X\to Y\) is an scc-mapping. Then, necessarily, \(f\) is 1-sequence-covering.NEWLINENEWLINEFurther aspects involving these results are also discussed.