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Densely continuous forms, pointwise topology and cardinal functions

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Abstract

We consider the space D(X, Y) of densely continuous forms introduced by Hammer and McCoy [5] and investigated also by Holá [6]. 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 τ- p . The largest part of the paper is devoted to the study of various cardinal functions for (D*(X), τ p ), in particular: character, pseudocharacter, weight, density, cellularity, diagonal degree, π-weight, π-character, netweight etc.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, Bratislava, SK-81473, Slovakia

    Peter Vadovič

  2. Faculty of industrial technologies in Púchov, Trenin university of Alexander Dubček, Ivana Krasku 491/30, Púchov, SK-02001, Slovakia

    Dušan Holý

Authors
  1. Dušan Holý
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  2. Peter Vadovič
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Corresponding author

Correspondence to Dušan Holý.

Additional information

This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-006904. The authors would like to thank Ľubica Holá for suggestions and comments.

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Holý, D., Vadovič, P. Densely continuous forms, pointwise topology and cardinal functions. Czech Math J 58, 79–92 (2008). https://doi.org/10.1007/s10587-008-0006-y

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  • DOI: https://doi.org/10.1007/s10587-008-0006-y

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