Skip to main content
SpringerLink
Log in

Weak Normality Forms outside a Diagonal

  • Published:
Moscow University Mathematics Bulletin Aims and scope

Abstract

In a certain model of ZFC set theory, it is proved that regular, \(F_{\sigma}\)-paranormal outside the diagonal, and countably compact spaces are first-countable (satisfying the first axiom of countability) and compact.

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.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. R. Engelking, General Topology (PWN, Warsaw, 1977).

    MATH  Google Scholar 

  2. A. V. Arhangel’skiǐ and A. P. Kombarov, ‘‘On \(\nabla\)-normal spaces’’, Topol. Its Appl. 35, 121–126 (1990). https://doi.org/10.1016/0166-8641(90)90097-L

    Article  Google Scholar 

  3. D. V. Malykhin, ‘‘A countably compact \(\nabla\)-normal space has a countable character,’’ Vestn. Mosk. Univ., Ser. 1: Mat., Mekh., No. 5, 31–33 (1997).

  4. P. Nyikos, ‘‘Problem section: Problem B,’’ Topol. Proc. 9, 367–367 (1984).

    Google Scholar 

  5. V. M. Ivanova, ‘‘To the theory of spaces of subsets,’’ Dokl. Akad. Nauk SSSR 101, 601–603 (1955).

    MathSciNet  Google Scholar 

  6. N. Kemoto, ‘‘Normality and countable paracompactness of hyperspaces of ordinals,’’ Topol. Its Appl. 154, 358–363 (2007). https://doi.org/10.1016/j.topol.2006.04.017

    Article  MathSciNet  MATH  Google Scholar 

  7. A. P. Kombarov, ‘‘On two properties of normality type,’’ Math. Notes 94, 440–443 (2013). https://doi.org/10.1134/S0001434613090149

    Article  MathSciNet  MATH  Google Scholar 

  8. T. Eisworth and P. Nyikos, ‘‘First countable, countably compact spaces and the continuum hypothesis,’’ Trans. Am. Math. Soc. 357, 4269–4399 (2005). https://doi.org/10.1090/S0002-9947-05-04034-1

    Article  MathSciNet  MATH  Google Scholar 

  9. A. P. Kombarov, ‘‘On \(F_{\sigma}\)-\({\delta}\)-normality and hereditary \({\delta}\)-normality,’’ Topol. Its Appl. 91, 221–226 (1999). https://doi.org/10.1016/S0166-8641(97)00205-8

    Article  MathSciNet  MATH  Google Scholar 

  10. K. Kunen, ‘‘Combinatorics,’’ in Handbook of Mathematical Logic, Ed. by K. J. Barwise (North-Holland, Amsterdam, 1977), pp. 371–403.

    Google Scholar 

  11. A. V. Arkhangelskii, ‘‘Structure and classification of topological spaces and cardinal invariants,’’ Russ. Math. Surv. 33, 33–96 (1978). https://doi.org/10.1070/RM1978v033n06ABEH003884

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chair of General Topology and Geometry, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119992, Moscow, Russia

    A. P. Kombarov

Authors
  1. A. P. Kombarov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. P. Kombarov.

Ethics declarations

The author declares that he has no conflicts of interest.

Additional information

Translated by I. Tselishcheva

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kombarov, A.P. Weak Normality Forms outside a Diagonal. Moscow Univ. Math. Bull. 77, 46–48 (2022). https://doi.org/10.3103/S002713222201003X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S002713222201003X

Keywords:

Search

Navigation