Analytic functions are $ℐ$-density continuous

Ciesielski, Krzysztof, and Larson, Lee. "Analytic functions are $\mathcal {I}$-density continuous." Commentationes Mathematicae Universitatis Carolinae 35.4 (1994): 645-652. <http://eudml.org/doc/247596>.

@article{Ciesielski1994,
abstract = {A real function is $\mathcal \{I\}$-density continuous if it is continuous with the $\mathcal \{I\}$-density topology on both the domain and the range. If $f$ is analytic, then $f$ is $\mathcal \{I\}$-density continuous. There exists a function which is both $C^\infty $ and convex which is not $\mathcal \{I\}$-density continuous.},
author = {Ciesielski, Krzysztof, Larson, Lee},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {analytic function; $\mathcal \{I\}$-density continuous; $\mathcal \{I\}$-density topology; infinitely differentiable function; -density continuous functions; -density topology; convex function},
language = {eng},
number = {4},
pages = {645-652},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Analytic functions are $\mathcal \{I\}$-density continuous},
url = {http://eudml.org/doc/247596},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Ciesielski, Krzysztof
AU - Larson, Lee
TI - Analytic functions are $\mathcal {I}$-density continuous
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 4
SP - 645
EP - 652
AB - A real function is $\mathcal {I}$-density continuous if it is continuous with the $\mathcal {I}$-density topology on both the domain and the range. If $f$ is analytic, then $f$ is $\mathcal {I}$-density continuous. There exists a function which is both $C^\infty $ and convex which is not $\mathcal {I}$-density continuous.
LA - eng
KW - analytic function; $\mathcal {I}$-density continuous; $\mathcal {I}$-density topology; infinitely differentiable function; -density continuous functions; -density topology; convex function
UR - http://eudml.org/doc/247596
ER -