It is shown that the class of real functions continuous
with respect to the deep-*I*-density topology on the range and the density
topology on the domain coincides with the class of all constant functions.
This determines of the last class from the sixteen classes
of continuous functions
C(T_{1},T_{2})
={f:(**R**,T_{1})-->(**R**,T_{2})},
where T_{i} stands for ordinary, density, *I*-density or
deep-*I*-density
topology
[K. Ciesielski, L. Larson,
Various continuities with the density and
*I*-density topologies,
* Real Anal. Exchange 17 * (1991-92), 183-210].

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**Last modified April 30, 1999.**