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Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 173–178 | Cite as

A Note on Separating Function Sets

  • R. Buzyakova
  • O. Okunev
Article
  • 10 Downloads

Abstract

We study separating function sets. We find some necessary and sufficient conditions for C p (X) or C p 2 (X) to have a point-separating subspace that is a metric space with certain nice properties. One of the corollaries to our discussion is that for a zero-dimensional X, C p (X) has a discrete point-separating space if and only if C p 2 (X) does.

Keywords and phrases

Cp(X) discrete space point-separating set spread i-weight σ-product 

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References

  1. 1.
    A. Arhangelskii, Topological Function Spaces, Vol. 78 of Mathematics and Its Applications (Academic, Dordrecht, 1992).CrossRefGoogle Scholar
  2. 2.
    R. Engelking, General Topology (PWN, Warszawa, 1977).zbMATHGoogle Scholar
  3. 3.
    V. V. Fedorchuk, “A compact having a cardinality of continuum with no convergent sequences,” Math. Proc. Cambridge Phil. Soc. 81, 177–181 (1977).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    S. Gulko and T. Hmyleva, “Compactaness is not preserved by t-equivalence,” Mat. Zam. 39, 895–903 (1986).Google Scholar
  5. 5.
    A. V. Ivanov, “On bicompacta with hereditary separable finite powers,” Dokl. Akad. Nauk SSSR 243, 1109–1112 (1978).MathSciNetGoogle Scholar
  6. 6.
    S. Mardesic, “On covering dimension and inverse limits of compact spaces,” Illinois J. Math. 4, 278–291 (1960).MathSciNetzbMATHGoogle Scholar
  7. 7.
    P. Zenor, “HereditaryM-separability and the hereditaryM-Lindelöf property in product spaces and function spaces,” Fund. Math. 106, 175–180 (1980).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Independent researcherMiami, FloridaUSA
  2. 2.Facultad de Ciencias Fisico-MatematicasBenemrita Universidad Autonoma de PueblaPueblaMexico

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