On topological groups with remainder of character k

Maddalena Bonanzinga, Maria Vittoria Cuzzupè

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.

 


Keywords

character; compactification; π-base; remainder; topological group

Subject classification

54H11; 54A25; 54B05

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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.

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Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt