Abstract

We investigate some closure properties of the space $C(X)$ of the continuous real-valued functions on a Tychonoff space $X$ endowed with the compact-open topology and the pointwise convergence topology.

Keywords: Reznichenko property, Pytkeev property, $k$-cover, countable (strong) fan tightness, groupability, compact-open topology, pointwise convergence topology, selection principles.

MSC: 54C35, 54D20

Pages:  57$-$70     

Volume  58 ,  Issue  1$-$2 ,  2006