On homeomorphisms of density type topologies generated by functions

Małgorzata Filipczak; Tomasz Filipczak

doi:10.2478/v10127-010-0014-9

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On homeomorphisms of density type topologies generated by functions

Tatra Mountains Mathematical Publications

Volume 46 (2010): Issue 1 (August 2010)

By: Małgorzata Filipczak and Tomasz Filipczak

Open Access

|Nov 2012

Abstract

The paper is concerned with homeomorphisms on topological spaces (ℝ, Tƒ), where Tƒ is a generalization of the density topology generated by a function ƒ. It is shown that the density topology is not homeomorphic with any other topology Tƒ and that, under some assumptions, homeomorphic ƒ-density topologies have to be comparable.

References

[1] FILIPCZAK, M.-FILIPCZAK, T.: A generalization of the density topology, Tatra Mt. Math. Publ. 34 (2006), 37-47.
Search in Google Scholar
[2] FILIPCZAK, M.-FILIPCZAK, T.: On f-density topologies, Topology Appl. 155 (2008), 1980-1989.10.1016/j.topol.2007.04.024
Search in Google Scholar
[3] FILIPCZAK, M.-FILIPCZAK, T.: Density topologies generated by functions and by sequences, Tatra Mt. Math. Publ. 40 (2008), 103-115.
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[4] FILIPCZAK, M.-FILIPCZAK, T.: On the comparison of the density type topologies generatedby sequences and by functions, Comment Math. 49 (2009), 161-170.
Search in Google Scholar
[5] FILIPCZAK, M.-FILIPCZAK, T.-HEJDUK, J.: On the comparison of the density typetopology, Atti Sem. Mat. Fis. Univ. Modena 52 (2004), 37-46.
Search in Google Scholar
[6] FILIPCZAK,M.-HEJDUK, J.: On topologies associated with the Lebesgue measure, Tatra Mt. Math. Publ. 28 (2004), 187-197.
Search in Google Scholar
[7] FILIPCZAK, M.-HEJDUK, J.-WILCZY´NSKI, W.: On homeomorphisms of the densitytype topologies, Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 45 (2005), 151-159.
Search in Google Scholar
[8] NATANSON, I. P.: Theory of Functions of a Real Variable (2nd ed.), Frederick Ungar Publ. Co., New York. 1961.
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Articles in this issue

DOI: https://doi.org/10.2478/v10127-010-0014-9 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

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Language: English

Page range: 7 - 13

Published on: Nov 13, 2012

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

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© 2012 Małgorzata Filipczak, Tomasz Filipczak, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Volume 46 (2010): Issue 1 (August 2010)