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Densely continuous forms, pointwise topology and cardinal functions

Dušan Holý, Peter Vadovič (2008)

Czechoslovak Mathematical Journal

We consider the space D ( X , Y ) of densely continuous forms introduced by Hammer and McCoy and investigated also by Holá . 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,...

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