Displaying similar documents to “Remarks on density topology and its category analogue”

Density covers

A. M. Bruckner, Charles L. Thorne (1973)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Pointwise density topology

Magdalena Górajska (2015)

Open Mathematics

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The paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise...

A category Ψ-density topology

Władysław Wilczyński, Wojciech Wojdowski (2011)

Open Mathematics

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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...