# On the generalization of density topologies on the real line

In: Mathematica Slovaca, vol. 64, no. 5
Jacek Hejduk - Renata Wiertelak

## Details:

Year, pages: 2014, 1267 - 1276
Keywords:
lower density operator, topology generated by lower density operator, density topology
The paper concerns the density points with respect to the sequences of intervals tending to zero in the family of Lebesgue measurable sets. It shows that for some sequences analogue of the Lebesgue density theorem holds. Simultaneously, this paper presents proof of theorem that for any sequence of intervals tending to zero a relevant operator $ΦJ$ generates a topology. It is almost but not exactly the same result as in the category aspect presented in [WIERTELAK, R.: \textit{A generalization of density topology with respect to category}, Real Anal. Exchange \textbf{32} (2006/2007), 273–286]. Therefore this paper is a continuation of the previous research concerning similarities and differences between measure and category.
How to cite:
ISO 690:
Hejduk, J., Wiertelak, R. 2014. On the generalization of density topologies on the real line. In Mathematica Slovaca, vol. 64, no.5, pp. 1267-1276. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0274-y

APA:
Hejduk, J., Wiertelak, R. (2014). On the generalization of density topologies on the real line. Mathematica Slovaca, 64(5), 1267-1276. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0274-y