Essential subgroups of topological groups |
| |
Authors: | Elena Boschi Dikran Dikranjan |
| |
Affiliation: | 1. Dipartimento di Matematica e Informatica , Università di Udine , Via delle Scienze 206, Udine, 33100, Italy E-mail: boschi@dimi.uniud.it;2. Dipartimento di Matematica e Informatica , Universitá di Udine , Via delle Scienze 206, Udine, 33100, Italy E-mail: dikranja@dimi.uniud.it |
| |
Abstract: | We study the class Wof Hausdorff topological groups Gfor which the following two cardinal invariants coincide ES(G)=min{|H|:H≤ Gdense and essential} TD(G)=min{|H|:H≤ Gtotally dense} We prove that W contains the following classes:locally compact abelian groups, compact connected groups, countably compact totally discon¬nected abelian groups, topologically simple groups, locally compact Abelian groups when endowed with their Bohr topology, totally minimal abelian groups and free Abelian topological groups. For all these classes we are also able to giv ean explicit computation of the common value of ESand TD. |
| |
Keywords: | locally compact group essential subgroup totally dense subgroup Pontryagin duality |
|
|