In the paper we investigate topological properties of a topological Brandt λ0-extension B0λ(S) of a semitopological monoid S with zero. In particular we prove that for every Tychonoff pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) semitopological monoid S with zero there exists a unique semiregular pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) extension B0λ(S) of S and establish their Stone-Cˇ ech and Bohr compactifications. We also describe a category whose objects are ingredients in the constructions of pseudocompact (resp., countably compact, sequentially compact, compact) topological Brandt λ0- extensions of pseudocompact (resp., countably compact, sequentially compact, compact) semitopological monoids with zeros.
@article{bwmeta1.element.doi-10_2478_taa-2013-0007,
author = {Oleg Gutik and Kateryna Pavlyk},
title = {
On pseudocompact topological Brandt $\lambda$
0
-extensions of semitopological monoids
},
journal = {Topological Algebra and its Applications},
volume = {1},
year = {2013},
pages = {60-79},
zbl = {1291.22003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_taa-2013-0007}
}
Oleg Gutik; Kateryna Pavlyk.
On pseudocompact topological Brandt λ
0
-extensions of semitopological monoids
. Topological Algebra and its Applications, Tome 1 (2013) pp. 60-79. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_taa-2013-0007/
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