Large and small sets with respect to homomorphisms and products of groups

Riccardo Gusso

Italy

Università di Venezia

Dipartimento di Matematica Applicata

Submitted: 2013-12-26

|

Accepted: 2013-12-26

|

Published: 2002-10-01

DOI: https://doi.org/10.4995/agt.2002.2059
Funding Data

Downloads

Keywords:

Group, Large set, Small set, P-small set, Homomorphism, Direct product

Supporting agencies:

This research was not funded

Abstract:

We study the behaviour of large, small and medium subsets with respect to homomorphisms and products of groups. Then we introduce the definition af a P-small set in abelian groups and we investigate the relations between this kind of smallness and the previous one, giving some examples that distinguish them.
Show more Show less

References:

G. Artico, V.I Malykhin, U. Marconi, Some large and small sets in topological groups, Math. Pannon. 12 (2001), nº.2, 157-165.

A. Bella, V.I Malykhin, On certain subsets of a group, Questions and answers in General Topology 17 (1999), 183-197.

A. Bella, V.I Malykhin, On certain subsets of a group II, Questions and answers in General Topology 19 (2001), 81-94.

M. Cotlar, R. RIcabarra, On the existence of characters in topological groups, Amer. J. Math. 76 (1954), 375-388. http://dx.doi.org/10.2307/2372579

D. Dikranjan, U. Marconi, R. Moresco, Groups with a small set of generators, to appear in the Proceedings of the international conference “Function spaces, proximities and quasi-uniformities” on the occasion of Som Naimpally’s 70 birthday. Caserta, September, 14-18, 2001.

Dikran N. Dikranjan, Ivan R. Prodanov, Luchezar N. Stoyanov, Topological Groups: Characters, Dualities and Minimal Group Topologies, Pure and Applied Mathematics, Vol. 130 (Marcel Dekker Inc. New York-Basel, 1989).

R. Ellis, H. Keynes, Bohr compactification and a result of Folner, Israel J. Math. 12 (1972), 314-330. http://dx.doi.org/10.1007/BF02790758

E. Folner, On groups with full Banach mean value, Math. Scand. 3 (1955), 243-254.

Show more Show less