Tightness of function spaces

Abstract

The purpose of this paper is to give higher cardinality versions of countable fan tightness of function spaces obtained by A. Arhangel’skiı. Let vet(X), ωH(X) and H(X) denote respectively the fan tightness, ω-Hurewicz number and Hurewicz number of a space X, then vet(Cp(X)) = ωH(X) = sup{H(Xn) : n 2 N}.

Keywords

• Function spaces
• Fan tightness
• Hurewicz spaces
• Cardinal functions