Spaces of continuous step functions over LOTS

Raushan Z. Buzyakova

Fundamenta Mathematicae, Tome 189 (2006), p. 25-35 / Harvested from The Polish Digital Mathematics Library

Résumé

We investigate spaces $C_{p} (\cdot, n)$ over LOTS (linearly ordered topological spaces). We find natural necessary conditions for linear Lindelöfness of $C_{p} (\cdot, n)$ over LOTS. We also characterize countably compact LOTS whose $C_{p} (\cdot, n)$ 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.

Publié le : 2006-01-01

Zbl 1111.54017

EUDML-ID : urn:eudml:doc:283251

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     author = {Raushan Z. Buzyakova},
     title = {Spaces of continuous step functions over LOTS},
     journal = {Fundamenta Mathematicae},
     volume = {189},
     year = {2006},
     pages = {25-35},
     zbl = {1111.54017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-1-2}
}

Raushan Z. Buzyakova. Spaces of continuous step functions over LOTS. Fundamenta Mathematicae, Tome 189 (2006) pp. 25-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-1-2/