Kodai Mathematical Journal

Local properties on the remainders of the topological groups

Fucai Lin

Full-text: Open access

Abstract

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 bG$\backslash$G has locally a k-space with a point-countable k-network and π-character of bG$\backslash$G is countable, then G and bG are separable and metrizable; (2) If bG$\backslash$G has locally a δθ-base, then G and bG are separable and metrizable; (3) If bG$\backslash$G 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 [16].

Article information

Source
Kodai Math. J., Volume 34, Number 3 (2011), 505-518.

Dates
First available in Project Euclid: 10 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1320935556

Digital Object Identifier
doi:10.2996/kmj/1320935556

Mathematical Reviews number (MathSciNet)
MR2855837

Zentralblatt MATH identifier
1234.54046

Citation

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


Export citation