We construct a set B and homeomorphism f where f and have property N such that the symmetric difference between the sets of density points and of f-density points of B is uncountable.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-2-4,
author = {Josh Campbell and David Swanson},
title = {Construction of an Uncountable Difference between $\Phi$(B) and $$\Phi$\_f(B)$
},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {56},
year = {2008},
pages = {121-130},
zbl = {1151.28300},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-2-4}
}
Josh Campbell; David Swanson. Construction of an Uncountable Difference between Φ(B) and $Φ_f(B)$
. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) pp. 121-130. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-2-4/