View More View Less
  • 1 Universidad Autónoma Metropolitana, Av. San Rafael Atlixco, 186, Col. Vicentina, Iztapalapa C.P. 09340, Mexico D.F., Mexico
Full access

Abstract

We prove that, for any cofinally Polish space X, every locally finite family of non-empty open subsets of X is countable. It is also established that Lindelöf domain representable spaces are cofinally Polish and domain representability coincides with subcompactness in the class of σ-compact spaces. It turns out that, for a topological group G whose space has the Lindelöf Σ-property, the space G is domain representable if and only if it is Čech-complete. Our results solve several published open questions.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1]

    Arhangel'skii, A. and Tkachenko, M., Topological Groups and Related Structures, Atlantis Press, Amsterdam, 2008.

  • [2]

    Aarts, J. M. and Lutzer, D. J., Completeness properties designed for recognizing Baire spaces, Dissertationes Math., 116 (1974), 143.

    • Search Google Scholar
    • Export Citation
  • [3]

    Bennett, H. J. and Lutzer, D. J., Domain-representable spaces, Fund. Math., 189 (2006), 255268.

  • [4]

    Bennett, H. J. and Lutzer, D. J., Domain-representability of certain complete spaces, Houston J. Math., 34 (3) (2008), 753772.

  • [5]

    Blanck, J., Domain representability of metric spaces, Ann. Pure Appl. Logic, 83 (1997), 225247.

  • [6]

    Blanck, J., Domain representations of topological spaces, Theoretical Comp. Sci., 247 (2000), 229255.

  • [7]

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

  • [8]

    Fleissner, W., Tkachuk, V. V. and Yengulalp, L., Every scattered space is subcompact, Topology Appl., 160 (12) (2013), 13051312.

  • [9]

    Fleissner, W. and Yengulalp, L., When Cp(X) is domain representable, Fund. Math., 223 (2013), 6581.

  • [10]

    Fleissner, W. and Yengulalp, L., From subcompact to domain representable, Topology Appl., 195 (2015), 174195.

  • [11]

    de Groot, J., Subcompactness and the Baire Category Theorem, Indag. Math., 22 (1963), 761767.

  • [12]

    Martin, K., Topological games in domain theory, Topology Appl., 129 (2003), 177186.

  • [13]

    van Mill, J. and Tkachuk, V. V., Every k-separable Čech-complete space is subcompact, RACSAM, 109 (2015), 6571.

  • [14]

    Niknejad, J., Tkachuk, V. V. and Yengulalp, L., Polish factorizations, cosmic spaces and domain representability, Bull. Belg. Math. Soc., 25 (3) (2018), 439452.

    • Search Google Scholar
    • Export Citation
  • [15]

    Önal, S. and Vural, C., Every monotonically normal Čech-complete space is subcompact, Topology Appl., 176 (2014), 3542.

  • [16]

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

  • [17]

    Uspenskij, V. V., A topological group generated by a Lindelöf Σ-space has the Souslin property (in Russian), Doklady AN SSSR, 265 (4) (1982), 823826.

    • Search Google Scholar
    • Export Citation

  • Impact Factor (2018): 0.309
  • Mathematics (miscellaneous) SJR Quartile Score (2018): Q3/li>
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21

Language: English, French, German

Founded in 1966
Publication: One volume of four issues annually
Publication Programme: 2020. Vol. 57.
Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Mathematical Reviews
  • Referativnyi Zhurnal/li>
  • Research Alert
  • Science Citation Index Expanded (SciSearch)/li>
  • SCOPUS
  • The ISI Alerting Services

 

Subscribers can access the electronic version of every printed article.

Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

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

The author instruction is available in PDF.

Please, download the file from HERE

Manuscript submission: HERE