On topological groups with remainder of character k

Authors

  • Maddalena Bonanzinga University of Messina
  • Maria Vittoria Cuzzupè University of Messina

DOI:

https://doi.org/10.4995/agt.2016.4376

Keywords:

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

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.

 

Downloads

Download data is not yet available.

Author Biography

Maddalena Bonanzinga, University of Messina

Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra

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.

Downloads

Published

2016-04-12

How to Cite

[1]
M. Bonanzinga and M. V. Cuzzupè, “On topological groups with remainder of character k”, Appl. Gen. Topol., vol. 17, no. 1, pp. 51–55, Apr. 2016.

Issue

Section

Regular Articles