Ψ-density point of a Lebesgue measurable set was introduced by Taylor in [Taylor S.J., On strengthening the Lebesgue Density Theorem, Fund. Math., 1958, 46, 305–315] and [Taylor S.J., An alternative form of Egoroff’s theorem, Fund. Math., 1960, 48, 169–174] as an answer to a problem posed by Ulam. We present a category analogue of the notion and of the Ψ-density topology. We define a category analogue of the Ψ-density point of the set A at a point x as the Ψ-density point at x of the regular open representation of A.
@article{bwmeta1.element.doi-10_2478_s11533-011-0069-0,
author = {W\l adys\l aw Wilczy\'nski and Wojciech Wojdowski},
title = {A category $\Psi$-density topology},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {1057-1066},
zbl = {1234.54008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0069-0}
}
Władysław Wilczyński; Wojciech Wojdowski. A category Ψ-density topology. Open Mathematics, Tome 9 (2011) pp. 1057-1066. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0069-0/
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