Complete systems, elementary submodels and the tightness of upper hyperspaces |
| |
Authors: | Debora Di Caprio |
| |
Affiliation: | Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario M3J 1P3, Canada |
| |
Abstract: | We introduce and study some completeness properties for systems of open coverings of a given topological space. A Hausdorff space admitting a system of cardinality κ satisfying one of these properties is of type Gκ. Hence, we define several new variants of the ?ech number and use elementary submodels to determine further results. We introduce M-hulls and M-networks, for M elementary submodel. As an application, we give estimates for both the tightness and the Lindelöf number of a generic upper hyperspace. Two recent results of Costantini, Holá and Vitolo on the tightness of co-compact hyperspaces follow from ours as corollaries. |
| |
Keywords: | primary, 54A25, 03C98 secondary, 54B20 |
本文献已被 ScienceDirect 等数据库收录! |
|