| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4661199 | Topology and its Applications | 2006 | 5 Pages |
Abstract
Boris Shapirovskii posed the following question: “Suppose a continuous mapping from one compact space onto another is given. Suppose that the π-character of any point in the domain is greater than the weight of the target space. Will there be two disjoint closed sets in the domain mapping onto?”. There is a zero-dimensional counterexample (Corollary 12), but the one cardinal up version is true in zero-dimensional case (Corollary 14). Nevertheless, there always will be two disjoint open sets mapping densely (Theorem 7).
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
