Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 58: Issue 3
A Corson Compact Space is Countable if the Complement of its Diagonal is Functionally Countable
Author:
Vladimir V. Tkachuk Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco, 186, Col. Vicentina, Iztapalapa C.P. 09340, Mexico D.F., Mexico

Search for other papers by Vladimir V. Tkachuk in
Current site
Google Scholar
PubMed Close
Pages:
398–407
Online Publication Date:
27 Sep 2021
Publication Date:
27 Sep 2021
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2021.58.3.1508
Keywords:
Corson compact space; scattered space; functionally countable space; diagonal; metrizability; separable space; P -space
Restricted access

A space X is called functionally countable if ƒ (X) is countable for any continuous function ƒ : X → Ø. Given an infinite cardinal k, we prove that a compact scattered space K with d(K) > k must have a convergent k+-sequence. This result implies that a Corson compact space K is countable if the space (K × K) \ ΔK is functionally countable; here ΔK = {(x, x): x ϵ K} is the diagonal of K. We also establish that, under Jensen’s Axiom ♦, there exists a compact hereditarily separable non-metrizable compact space X such that (X × X) \ ΔX is functionally countable and show in ZFC that there exists a non-separable σ-compact space X such that (X × X) \ ΔX is functionally countable.

  • [1]

    A. V. Arhangel’skii . Topological Function Spaces. Kluwer Acad. Publ., Dordrecht, 1992.

  • [2]

    B. Cascales and J. Orihuela . On compactness in locally convex spaces. Math. Z., 195:365–381, 1987.

  • [3]

    J. Chaber . Conditions which imply compactness in countably compact spaces. Bull. Acad. Pol. Sci. Ser.Math., 24:993–998, 1976.

  • [4]

    G. I. Chertanov . Products of linearly ordered spaces and continuous maps. Dokl. Akad. Nauk SSSR, 223:6:1322–1325, 1975.

  • [5]

    A. Dow and D. Guerrero Sánchez . Domination conditions under which a compact space is metrizable. Bull. Austral. Math. Soc., 91:502–507, 2015.

    • Search Google Scholar
    • Export Citation
  • [6]

    A. Dow and K.P. Hart . Compact spaces with a ℙ-diagonal. Indag. Math., 27(3):721–726, 2016.

  • [7]

    R. Engelking . General Topology. PWN, Warszawa, 1977.

  • [8]

    F. Galvin . Problem 6444. Amer. Math. Monthly, 90(9):648, 1983. Solution: Amer. Math. Monthly, 92(6):434, 1985.

  • [9]

    H. Z. Hdeib and C.M. Pareek . A generalization of scattered spaces. Topology Proc., 14:59–74, 1989.

  • [10]

    R. Levy and M. Matveev . Functional separability. Comment. Math. Univ. Carolinae, 51:4:705–711, 2010.

  • [11]

    J. T. Moore . A solution to the L space problem. J. Amer. Math. Soc., 19:3:717–736, 2006.

  • [12]

    A. Ostaszewski . On countably compact perfectly normal spaces. J. London Math. Soc., 14:505–516, 1976.

  • [13]

    A. Pelczynski and Z. Semadeni . Spaces of continuous functions III (Spaces C(Ω) for Ω without perfect subsets). Studia Math., 18:211–222, 1959.

    • Search Google Scholar
    • Export Citation
  • [14]

    W. Rudin . Continuous functions on compact spaces without perfect subsets. Proc. Amer. Math. Soc., 8:39–42, 1957.

  • [15]

    V. V. Tkachuk . A nice subclass of functionally countable spaces. Comment. Math. Univ. Carolinae, 59:3:399–409, 2018.

  • [16]

    V. V. Tkachuk . Some applications of exponentially separable spaces. Quaestiones Math., 43:10:1392–1403, 2020.

  • [17]

    V. V. Tkachuk . The extent of a weakly exponentially separable space can be arbitrarily large. Houston J. Math., 46:3:809–819, 2020.

  • [18]

    V. V. Tkachuk . A Cp -theory Problem Book. Topological and Function Spaces. Springer, New York, 2011.

  • [19]

    V. V. Tkachuk . A Cp -theory Problem Book. Special Features of Function Spaces. Springer, New York, 2014.

  • [20]

    V. V. Tkachuk . A Cp -Theory Problem Book. Compactness in Function Spaces. Springer, New York, 2015.

  • Collapse
  • Expand
Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333
E-mail: smh.studia@renyi.mta.hu

Indexing and Abstracting Services:

  • CABELLS Journalytics
  • CompuMath Citation Index
  • Essential Science Indicators
  • Mathematical Reviews
  • Science Citation Index Expanded (SciSearch)
  • SCOPUS
  • Zentralblatt MATH

2024  
Scopus  
CiteScore  
CiteScore rank  
SNIP  
Scimago  
SJR index 0.305
SJR Q rank Q3

2023  
Web of Science  
Journal Impact Factor 0.4
Rank by Impact Factor Q4 (Mathematics)
Journal Citation Indicator 0.49
Scopus  
CiteScore 1.3
CiteScore rank Q2 (General Mathematics)
SNIP 0.705
Scimago  
SJR index 0.239
SJR Q rank Q3

Studia Scientiarum Mathematicarum Hungarica
Publication Model Hybrid
Submission Fee none
Article Processing Charge 900 EUR/article (only for OA publications)
Printed Color Illustrations 40 EUR (or 10 000 HUF) + VAT / piece
Regional discounts on country of the funding agency World Bank Lower-middle-income economies: 50%
World Bank Low-income economies: 100%
Further Discounts Editorial Board / Advisory Board members: 50%
Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100%
Subscription fee 2025 Online subsscription: 796 EUR / 876 USD
Print + online subscription: 900 EUR / 988 USD
Subscription Information Online subscribers are entitled access to all back issues published by Akadémiai Kiadó for each title for the duration of the subscription, as well as Online First content for the subscribed content.
Purchase per Title Individual articles are sold on the displayed price.

Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Dec 2024 27 0 0
Jan 2025 18 0 0
Feb 2025 19 0 0
Mar 2025 9 0 0
Apr 2025 10 0 0
May 2025 1 0 0
Jun 2025 0 0 0