Paracompact locally Lindelöf spaces and \(L\)-systems. (English) Zbl 1074.54008
Summary: We establish relationships between paracompact locally Lindelöf spaces and all kinds of spaces with \(L\)-systems by means of closed mappings, weakly perfect mappings and quotient mappings. In particular, we obtain some characterizations of paracompact locally Lindelöf spaces. Interestingly, they are also characterized as weakly perfect inverse images of locally separable metric spaces.
MSC:
54D50 | \(k\)-spaces |
54D55 | Sequential spaces |
54C10 | Special maps on topological spaces (open, closed, perfect, etc.) |