Abstract

We investigate abstract boundedness in a topological space and demonstrate the importance of this notion in selection principles theory. Some applications to function spaces and hyperspaces are given. This approach sheds more light on several results scattered in the literature.

Keywords: Boundedness, $\Bbb B$-cover, $\gamma_{\Bbb B}$-cover, selection principles, topological games, partition symbol, countable fan tightness, countable strong fan tightness, $T$-tightness, $C_b(X)$, hyperspaces.

MSC: 54A25, 54B20, 54C35, 54D20, 03E02, 91A44.

Pages:  137$-$148     

Volume  60 ,  Issue  2 ,  2008