A category Ψ-density topology

Władysław Wilczyński; Wojciech Wojdowski

Open Mathematics (2011)

  • Volume: 9, Issue: 5, page 1057-1066
  • ISSN: 2391-5455

Abstract

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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 regular open representation of A.

How to cite

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Władysław Wilczyński, and Wojciech Wojdowski. "A category Ψ-density topology." Open Mathematics 9.5 (2011): 1057-1066. <http://eudml.org/doc/269476>.

@article{WładysławWilczyński2011,
abstract = {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.},
author = {Władysław Wilczyński, Wojciech Wojdowski},
journal = {Open Mathematics},
keywords = {Density point; Density topology},
language = {eng},
number = {5},
pages = {1057-1066},
title = {A category Ψ-density topology},
url = {http://eudml.org/doc/269476},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Władysław Wilczyński
AU - Wojciech Wojdowski
TI - A category Ψ-density topology
JO - Open Mathematics
PY - 2011
VL - 9
IS - 5
SP - 1057
EP - 1066
AB - 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.
LA - eng
KW - Density point; Density topology
UR - http://eudml.org/doc/269476
ER -

References

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