Atlas: Discrete $C^*$-embedded subsets of a locally compact Abelian group with its Bohr topology by Salvador Hernandez

Atlas home || Conferences | Abstracts | about Atlas

Special Session in Topological Methods
April 13-14, 1996
Courant Institute, New York University
New York, NY, USA

Organizers
L. Narici, E. Beckenstein, C. Traina

View Abstracts

Discrete C^*-embedded subsets of a locally compact Abelian group with its Bohr topology
by
Salvador Hernández
Universitat Jaume I
Coauthors: Jorge Galindo

In what follows G denotes a locally compact Abelian group and G⁺ denotes this group endowed with its Bohr topology.

Theorem If A is an infinite subset of G and K(A) denotes the compact-covering number of cl_G A. Then there exists a relatively discrete subset D of A with |D| = K(A) that is C-embedded in G⁺ and C^*-embedded in bG (the Bohr compactification of G).

Remark This result generalizes two analogous results of E. van Douwen in the cases in which G is discrete or the real line with its standard topology.

Date received: January 15, 1996