Spaces of continuous step functions over LOTS

Volume 192 / 2006

Raushan Z. Buzyakova Fundamenta Mathematicae 192 (2006), 25-35 MSC: 54C35, 54D20, 54F05, 54F65. DOI: 10.4064/fm192-1-2

Abstract

We investigate spaces $C_{\rm p}(\cdot, n)$ over LOTS (linearly ordered topological spaces). We find natural necessary conditions for linear Lindelöfness of $C_{\rm p}(\cdot , n)$ over LOTS. We also characterize countably compact LOTS whose $C_{\rm p}(\cdot, n)$ is linearly Lindelöf for each $n$. Both the necessary conditions and the characterization are given in terms of the topology of the Dedekind completion of a LOTS.

Authors

  • Raushan Z. BuzyakovaMathematics Department
    UNCG
    PO Box 26170
    Greensboro, NC 27402, U.S.A.
    e-mail

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