Kodai Mathematical Journal
- Kodai Math. J.
- Volume 34, Number 3 (2011), 505-518.
Local properties on the remainders of the topological groups
When does a topological group G have a Hausdorff compactification bG with a remainder belonging to a given class of spaces? In this paper, we mainly improve some results of A. V. Arhangel'skiĭ and C. Liu's. Let G be a non-locally compact topological group and bG be a compactification of G. The following facts are established: (1) If bGG has locally a k-space with a point-countable k-network and π-character of bGG is countable, then G and bG are separable and metrizable; (2) If bGG has locally a δθ-base, then G and bG are separable and metrizable; (3) If bGG has locally a quasi-Gδ-diagonal, then G and bG are separable and metrizable. Finally, we give a partial answer for a question, which was posed by C. Liu in .
Kodai Math. J., Volume 34, Number 3 (2011), 505-518.
First available in Project Euclid: 10 November 2011
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Lin, Fucai. Local properties on the remainders of the topological groups. Kodai Math. J. 34 (2011), no. 3, 505--518. doi:10.2996/kmj/1320935556. https://projecteuclid.org/euclid.kmj/1320935556