Density-to-deep-I-density continuous functions


Krzysztof Ciesielski

Real Anal. Exchange 17 (1991-92), 171-182

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(T1,T2) ={f:(R,T1)-->(R,T2)}, where Ti 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.