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Comparison of density topologies on the real line

  • Renata Wiertelak EMAIL logo
Published/Copyright: February 9, 2018
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Abstract

In this paper will be considered density-like points and density-like topology in the family of Lebesgue measurable subsets of real numbers connected with a sequence 𝓙= {Jn}n∈ℕ of closed intervals tending to zero. The main result concerns necessary and sufficient condition for inclusion between that defined topologies.


Communicated by David Buhagiar


References

[1] Ciesielski, K.—Larson, L.—Ostaszewski, K.: 𝓘-density continuous functions, Mem. Amer. Math. Soc. 107(515) (1994).10.1090/memo/0515Search in Google Scholar

[2] Filipczak, M.—Filipczak, T.—Hejduk, J.: On the comparison of the density type topologies, Atti Sem. Mat. Fis. Univ. Modena LII (2004), 1–11.Search in Google Scholar

[3] Filipczak, M.—Hejduk, J.; On topologies associated with the Lebesgue measure, Tatra Mt. Math. Publ. 28 (2004), 187–197.Search in Google Scholar

[4] Hejduk, J.—Loranty, A.—Wiertelak, R.: On 𝓙-continuous functions, Tatra Mt. Math. Publ., to appear.10.1515/tmmp-2016-0004Search in Google Scholar

[5] Hejduk, J.—Wiertelak, R.: On the generalization of density topologies on the real line, Math. Slovaca 64 (2014), 1267–1276.10.2478/s12175-014-0274-ySearch in Google Scholar

Received: 2015-11-12
Accepted: 2016-5-27
Published Online: 2018-2-9
Published in Print: 2018-2-23

© 2018 Mathematical Institute Slovak Academy of Sciences

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