Density continuous transformations on R2


Krzysztof Ciesielski & Wladyslaw Wilczynski

Real Anal. Exchange 20 (1994-95), 102-118

In the paper we study transformations from R2 into R and from R2 into R2 continuous with respect to different density topologies on the domain and range. In the former case the range will always be equipped with the one-dimensional density topology and the domain with either ordinary density or strong density topology. In the later case the domain and the range will be equipped simultaneously with the ordinary density or strong density topology. We will investigate the relations between these classes and with the class of ordinary continuous transformations. We will also examine relation between the (strong) density continuity of f:R2-->R and of f(.,y), f(x,.). Similar question will be considered for transformations F=(f,g):R2-->R2 and their coordinate functions f and g.

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Last modified April 24, 1999.