Spaces of continuous step functions over LOTS
Volume 192 / 2006
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.
