| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4661509 | Topology and its Applications | 2007 | 9 Pages |
Abstract
For a Tychonoff space X, we denote by Cp(X) the space of all real-valued continuous functions on X with the topology of pointwise convergence. We show the following: (1) for the closed unit interval I, Cp(I) does not have the weak sequence selection property; (2) if X is a QN-space, then Cp(X) is an α1-space. These results answer problems posed by M. Scheepers. Also we give characterizations of the α1-property, the α2-property (i.e. the sequence selection property) and the weak sequence selection property of Cp(X) in terms of covering properties of X.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
