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We investigate spaces over LOTS (linearly ordered topological spaces). We find natural necessary conditions for linear Lindelöfness of over LOTS. We also characterize countably compact LOTS whose 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.
Raushan Z. Buzyakova. "Spaces of continuous step functions over LOTS." Fundamenta Mathematicae 192.1 (2006): 25-35. <http://eudml.org/doc/283251>.
@article{RaushanZ2006, abstract = {We investigate spaces $C_\{p\}(·,n)$ over LOTS (linearly ordered topological spaces). We find natural necessary conditions for linear Lindelöfness of $C_\{p\}(·,n)$ over LOTS. We also characterize countably compact LOTS whose $C_\{p\}(·,n)$ 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.}, author = {Raushan Z. Buzyakova}, journal = {Fundamenta Mathematicae}, keywords = {linearly ordered topological space; Dedekind completion; linearly Lindelöf; pointwise convergence}, language = {eng}, number = {1}, pages = {25-35}, title = {Spaces of continuous step functions over LOTS}, url = {http://eudml.org/doc/283251}, volume = {192}, year = {2006}, }
TY - JOUR AU - Raushan Z. Buzyakova TI - Spaces of continuous step functions over LOTS JO - Fundamenta Mathematicae PY - 2006 VL - 192 IS - 1 SP - 25 EP - 35 AB - We investigate spaces $C_{p}(·,n)$ over LOTS (linearly ordered topological spaces). We find natural necessary conditions for linear Lindelöfness of $C_{p}(·,n)$ over LOTS. We also characterize countably compact LOTS whose $C_{p}(·,n)$ 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. LA - eng KW - linearly ordered topological space; Dedekind completion; linearly Lindelöf; pointwise convergence UR - http://eudml.org/doc/283251 ER -