We construct an arc-analytic function (i.e. analytic on every real-analytic arc) in ℝ² which is analytic outside a nondiscrete subset of ℝ².
@article{bwmeta1.element.bwnjournal-article-apmv59z3p251bwm,
author = {Krzysztof Kurdyka},
title = {An arc-analytic function with nondiscrete singular set},
journal = {Annales Polonici Mathematici},
volume = {60},
year = {1994},
pages = {251-254},
zbl = {0804.32007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv59z3p251bwm}
}
Krzysztof Kurdyka. An arc-analytic function with nondiscrete singular set. Annales Polonici Mathematici, Tome 60 (1994) pp. 251-254. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv59z3p251bwm/
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