Uniform covers and compact images of metric spaces. (Chinese. English summary) Zbl 1117.54040
Summary: The structures of sequence-covering compact images of locally separable metric spaces are investigated by uniform covers, the main results are that (1) a space is a sequence-covering compact image of a locally separable metric space if and only if it has a uniform \(sn\)-network consisting of cosmic subspaces; (2) a space is a sequence-covering quotient compact image of a locally separable metric space if and only if it is a locally cosmic space and a sequence-covering quotient compact image of a metric space.
MSC:
| 54E20 | Stratifiable spaces, cosmic spaces, etc. |
| 54D20 | Noncompact covering properties (paracompact, Lindelöf, etc.) |
| 54D55 | Sequential spaces |
| 54D65 | Separability of topological spaces |
| 54E15 | Uniform structures and generalizations |
