On topological groups with remainder of character k
Submitted: 2015-11-23
|Accepted: 2016-01-04
|Published: 2016-04-12
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Keywords:
character, compactification, π-base, remainder, topological group
Supporting agencies:
Abstract:
In [A.V. Arhangel'skii and J. van Mill, On topological groups with a first-countable remainder, Top. Proc. 42 (2013), 157-163] it is proved that the character of a non-locally compact topological group with a first countable remainder doesn't exceed $\omega_1$ and a non-locally compact topological group of character $\omega_1$ having a compactification whose reminder is first countable is given. We generalize these results in the general case of an arbitrary infinite cardinal k.
References:
A. V. Arhangel'skii, Construction and classification of topological spaces and cardinal invariants, Uspehi Mat. Nauk. 33, no. 6 (1978), 29-84. https://doi.org/10.1070/RM1978v033n06ABEH003884
A.V. Arhangel'skii, On the cardinality of bicompacta satisfying the first axiom of countability, Doklady Acad. Nauk SSSR 187 (1969), 967-970.
A.V. Arhangel'skii and J. van Mill, On topological groups with a first-countable remainder, Topology Proc. 42 (2013), 157-163.
R. Engelking, General Topology, Heldermann Verlag, Berlin, second ed., 1989.
I. Juhász, Cardinal functions in topology--ten years later, Mathematical Centre Tract, vol. 123, Mathematical Centre, Amsterdam, 1980.
