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Keywords:
analytic function; $\Cal I$-density continuous; $\Cal I$-density topology
analytic function; $\Cal I$-density continuous; $\Cal I$-density topology
Summary:
A real function is $\Cal I$-density continuous if it is continuous with the $\Cal I$-density topology on both the domain and the range. If $f$ is analytic, then $f$ is $\Cal I$-density continuous. There exists a function which is both $C^\infty $ and convex which is not $\Cal I$-density continuous.
References:
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[2] Ciesielski K., Larson L.: The space of density continuous functions. Acta Math. Hung. 58 (1991), 289-296. MR 1153484 | Zbl 0757.26006
[3] Poreda W., Wagner-Bojakowska E., Wilczyński W.: A category analogue of the density topology. Fund. Math. 75 (1985), 167-173. MR 0813753
[4] Wilczyński W.: A generalization of the density topology. Real Anal. Exchange 8(1) (1982-83), 16-20.
[5] Wilczyński W.: A category analogue of the density topology, approximate continuity, and the approximate derivative. Real Anal. Exchange 10 (1984-85), 241-265. MR 0790803
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