Skip to main content
SpringerLink
Log in

Continuity in the density topology II

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

The paper deals with real functions of real variable continuous in the density topology on the domain and on the range. The set on which such functions preserve upper outer density is described. Also the class of homeomorphisms continuous in the density topology is considered. At last some problems of differentiability are analysed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bruckner A. M.,Density-preserving homeomorphisms and the theorem of Maximoff, Quart. J. Math. Oxford, (2),21 (1970), 337–347.

    Article  MATH  MathSciNet  Google Scholar 

  2. Bruckner A. M.,Differentiation of Real Functions, Lecture Notes in Mathematics659, Springer 1978.

  3. Filipczak F. M.,On the structure of the set of symmetric non-differentiability of a continuous function (in Polish), Lodz University, 1973.

  4. Niewiarowski J.,Density-preserving homeomorphisms, Fund. Math.,106 (1980), 77–87.

    MATH  MathSciNet  Google Scholar 

  5. Ostaszewski K.,Continuity in the density topology, Real Anal. Exchange, (1982), 259–270.

  6. Ostaszewski K.,Two modifications of the approximate derivative, Demonstratio Math.,15, No. 3 (1982), 899–911.

    MATH  MathSciNet  Google Scholar 

  7. Sindalovski G.,Some questions of continuity and differentiability of measurable functions (in Russian), Izv. Akad. Nauk SSSR (Math.)22 (1958), 395–432.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Washington, G.N.-50, 98195, Seattle, Washington, U.S.A.

    Krzysztof Ostaszewski

Authors
  1. Krzysztof Ostaszewski
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ostaszewski, K. Continuity in the density topology II. Rend. Circ. Mat. Palermo 32, 398–414 (1983). https://doi.org/10.1007/BF02848542

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02848542

Keywords

Search

Navigation