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DENSITY, SMITAL PROPERTY AND QUASICONTINUITY
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 97 / Issue 2 / April 2018
- Published online by Cambridge University Press:
- 04 December 2017, pp. 246-252
- Print publication:
- April 2018
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- Article
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Based on the abstract version of the Smital property, we introduce an operator
$DS$. We use it to characterise the class of semitopological abelian groups, for which addition is a quasicontinuous operation.
THE BAIRE PROPERTY IN THE REMAINDERS OF SEMITOPOLOGICAL GROUPS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 88 / Issue 2 / October 2013
- Published online by Cambridge University Press:
- 21 January 2013, pp. 301-308
- Print publication:
- October 2013
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It is proved that every remainder of a nonlocally compact semitopological group
$G$ is a Baire space if and only if 
$G$ is not Čech-complete, which improves a dichotomy theorem of topological groups by Arhangel’skiǐ [‘The Baire property in remainders of topological groups and other results’, Comment. Math. Univ. Carolin. 50(2) (2009), 273–279], and also gives a positive answer to a question of Lin and Lin [‘About remainders in compactifications of paratopological groups’, ArXiv: 1106.3836v1 [Math. GN] 20 June 2011]. We also show that for a nonlocally compact rectifiable space 
$G$ every remainder of 
$G$ is either Baire, or meagre and Lindelöf.
