Annali di Matematica Pura ed Applicata

, Volume 128, Issue 1, pp 317–323 | Cite as

Cϰ(X) and a property of (db)-spaces

  • Aaron R. Todd
Article

Summary

A new class of locally convex linear topological spaces, the (db)-spaees, recently defined by Robertson, Tweddle and Yeomans, interpolates the classes of Baire-like and unordered Baire-like spaces. Saxon and Narayanaswami have given convex metrizable spaces that distinguish among these classes. This paper gives a new characterization of (db)-spaces from which is extracted the class of b-spaces. This class interpolates the classes of α-spaces and α′-spaces of Lehner. Let Cϰ(X) be the space of all real-valued continuous functions on the completely regular Sausdorf space X, supplied with the topology of uniform convergence on compact sets of X. It is shown that Cϰ(X) is a b-space if and only if it is an α-space. A characterization of X for which Cϰ(X) is a (db)-space is unknown. Other open questions are stated in the paper.

Keywords

Continuous Function Topological Space Uniform Convergence Metrizable Space Linear Topological Space 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1981

Authors and Affiliations

  • Aaron R. Todd
    • 1
  1. 1.Staten Island

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