Resumen de Estructuras de grupo topológico en (Z,+)¹

Daniel de la Barrera Mayoral, Elena Martín Peinador

• We consider in this paper how diverse topological group structures there can be on the group of integers numbers. We survey some results from us and from other mathematitians as well, order to present in Z:

  1. A family of 2 ͑ group topologies witch are Hausdorff precompact (noncompact).

  2. A family of metrizable noncomplete nor precompact group topologies.

  3. A family of complete nonmetrizable topologies.

  We leave some open questions - for instance, the cardinality of the families described in 2. and 3.- which we are studying as a part of the Doctoral Dissertation of the author.