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Rendiconti del Circolo Matematico di Palermo

, Volume 42, Issue 3, pp 382–390 | Cite as

Spaces hereditarily of κ-type and point κ-type

  • Gary Grabner
  • Andrzej Szymanski
Article
  • 17 Downloads

Abstract

In this paper we discuss the structure of regular spaces hereditarily of κ-type and point κ-type. In particular, it is shown that a regular spaceX is hereditarily of point κ-type iff for everyp∈X there is a setE (possibly empty) of isolated points ofX such that (1)E∪{p} is compact and (2)X(E∪{p}, X)≤κ.

Ams Subj. Class.

54B05 54D30 54D50 point κ-type κ-type character open dense subspace 

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References

  1. [1]
    Arhangel'skii A.V.,On a class of spaces containing all metric and locally bicompact spaces, Dokl. Akad. Nauk SSSR151 (1963), 751–754=Soviet Math. Dokl.4 (1968), 1051–1055.MathSciNetGoogle Scholar
  2. [2]
    Arhangel'skii A.V.,Bicompact sets and the topology of spaces, Trudy Moskov. Mat. Obsc.13 (1965), 3–55=Trans. Moscow Math. Soc. (1965), 1–62.MathSciNetGoogle Scholar
  3. [3]
    Arhangel'skii A.V.,On hereditary properties, Gen. Top. and Appl. (1973), 39–46.Google Scholar
  4. [4]
    Fletcher P., Lindgren W.,θ-spaces Gen. Top. and Appl.9 (1957), 139–153.CrossRefMathSciNetGoogle Scholar
  5. [5]
    Hneriksen M., Isbell J.,Some properties of compactifications, Duke Math. J.25 (1957), 873–105.Google Scholar
  6. [6]
    Ismail M.,A note on a theorem of Arhangel'skii, Gen. Top. and Appl.9 (1978), 217–220.CrossRefMathSciNetGoogle Scholar
  7. [7]
    Juhasz I.,Cardinal functions in topology, Math. Centre Tracts34, Amsterdam (1971).Google Scholar
  8. [8]
    Pytkeev E.,Hereditarily plumed spaces, Math. Zametki28 (1980), 603–618.MATHMathSciNetGoogle Scholar
  9. [9]
    Sabella R.,Spaces in which compact sets have countable local bases, Proc. Amer. Math. Soc.48 (1975), 499–504.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Vaughan J.,Spaces of countable and point-countable type, Trans. Amer. Math. Soc.151 (1970), 341–351.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer 1993

Authors and Affiliations

  • Gary Grabner
    • 1
  • Andrzej Szymanski
    • 1
  1. 1.Department of MathematicsSlippery Rock UniversitySlippery Rock

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