Spaces of continuous step functions over 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 -