Spaces of continuous step functions over LOTS

Raushan Z. Buzyakova

Fundamenta Mathematicae (2006)

  • Volume: 192, Issue: 1, page 25-35
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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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 -

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