Czechoslovak Mathematical Journal, Vol. 58, No. 1, pp. 79-92, 2008

# Densely continuous forms, pointwise topology and cardinal functions

Peter Vadovic, Mathematical Institute, Slovak Academy of Sciences, Stefanikova 49, Bratislava SK-814 73, Slovakia, e-mail: vadovic@mat.savba.sk; Dusan Holy, Faculty of industrial technologies in Puchov, Trenin university of Alexander Dubcek, Ivana Krasku 491/30, Puchov SK-02001, Slovakia, e-mail: holy@fpt.tnuni.sk

Abstract: We consider the space $D(X,Y)$ of densely continuous forms introduced by Hammer and McCoy \cite5 and investigated also by Hola \cite6. We show some additional properties of $D(X,Y)$ and investigate the subspace $D^*(X)$ of locally bounded real-valued densely continuous forms equipped with the topology of pointwise convergence $\tau_p$. The largest part of the paper is devoted to the study of various cardinal functions for $(D^*(X),\tau_p)$, in particular: character, pseudocharacter, weight, density, cellularity, diagonal degree, $\pi$-weight, $\pi$-character, netweight etc.

Keywords: locally bounded densely continuous form, topology of pointwise convergence, cardinal function, weight, density, netweight, cellularity

Classification (MSC 2000): 54C60, 54A25, 54E15

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