Advertisement

Siberian Mathematical Journal

, Volume 47, Issue 2, pp 239–244 | Cite as

The property O n for finite seminormal functors

  • A. V. Ivanov
  • K. V. Matyushichev
Article
  • 13 Downloads

Abstract

We give a finite combinatorial test for finite seminormal functors to possess the property On and use it in establishing that in some cases this property leads to some well-known functors. For example, if some functor F possesses the property O2 then F2 coincides with either exp2 or the squaring functor. Hence we conclude that if F(Dω1) and Dω1 are homeomorphic then F2 is either exp2 or (·)2.

Keywords

compact space open mapping seminormal functor finite functor exponential functor infinite-to-one mapping 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ivanov A. V., “On functors of finite degree and κ-metrizable bicompact spaces,” Siberian Math. J., 42, No. 1, 52–58 (2001).CrossRefzbMATHGoogle Scholar
  2. 2.
    Ivanov A. V., “On power spectra and compositions of strictly epimorphic functors,” Trudy Petrozavodsk Univ. Mat., 7, 1–14 (2000).zbMATHGoogle Scholar
  3. 3.
    Shchepin E. V., “The topology of limit spaces of uncountable inverse spectra,” Uspekhi Mat. Nauk, 31, No. 5, 191–226 (1976).zbMATHMathSciNetGoogle Scholar
  4. 4.
    Shchepin E. V., “Functors and uncountable powers of compacta,” Uspekhi Mat. Nauk, 36, No. 3, 3–62 (1981).zbMATHMathSciNetGoogle Scholar
  5. 5.
    Fedorchuk V. V. and Filippov V. V., General Topology. Basic Constructions [in Russian], Moscow Univ., Moscow (1988).Google Scholar
  6. 6.
    Basmanov V. N., “Covariant functors, retracts, and dimension,” Dokl. Akad. Nauk SSSR, 271, No. 5, 1033–1036 (1983).zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. V. Ivanov
    • 1
  • K. V. Matyushichev
    • 1
  1. 1.Petrozavodsk State UniversityPetrozavodskRussia

Personalised recommendations