A category analogue of the density topology

W. Poreda; E. Wagner-Bojakowska; Władysław Wilczyński

Displaying similar documents to “A category analogue of the density topology”

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...

A topological proof of Denjoy-Stepanoff theorem

Jaroslav Lukeš (1978)

Časopis pro pěstování matematiky

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On the prolongation of restrictions of Baire 1 functions to functions which are quasicontinuous and approximately continuous

Zbigniew Grande (2009)

Colloquium Mathematicae

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Let I ⊂ ℝ be an open interval and let A ⊂ I be any set. Every Baire 1 function f: I → ℝ coincides on A with a function g: I → ℝ which is simultaneously approximately continuous and quasicontinuous if and only if the set A is nowhere dense and of Lebesgue measure zero.

Baire classification of ...-density and ...-approximately continous functions.

K. Ciesielski, Lee Larson (1995)

Forum mathematicum

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Two theorems on measurable sets and sets having the Baire property

Malgorzata Filipczak (1992)

Czechoslovak Mathematical Journal

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Category theorems concerning Z-density continuous functions

K. Ciesielski, L. Larson (1991)

Fundamenta Mathematicae

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The ℑ-density topology $T_{ℑ}$ on ℝ is a refinement of the natural topology. It is a category analogue of the density topology [9, 10]. This paper is concerned with ℑ-density continuous functions, i.e., the real functions that are continuous when the ℑ-densitytopology is used on the domain and the range. It is shown that the family $C_{ℑ}$ of ordinary continuous functions f: [0,1]→ℝ which have at least one point of ℑ-density continuity is a first category subset of C([0,1])= f: [0,1]→ℝ: f is continuous...