Abstract
We prove that for each Polish space X, the space C(X) of continuous real-valued functions on X satisfies (a strong version of) the Pytkeev property, if endowed with the compact-open topology. We also consider the Pytkeev property in the case where C(X) is endowed with the topology of pointwise convergence.
| Original language | English |
|---|---|
| Pages (from-to) | 563-571 |
| Number of pages | 9 |
| Journal | Houston Journal of Mathematics |
| Volume | 35 |
| Issue number | 2 |
| State | Published - 2009 |
Keywords
- Compact-open topology
- Metrizability
- Pointwise convergence
- Pytkeev property
- Strong Pytkeev property