The Hartman-Mycielski construction and topological monomorphisms

• Reyes, Boris ^[1] ; Tkachenko, Mikhail ^[2]
  1. [1] Universidad del Atlántico

     Universidad del Atlántico

     México

     
  2. [2] Universidad Autónoma Metropolitana

     Universidad Autónoma Metropolitana

     México

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 27, Nº. 2, 2026
• Idioma: inglés
• DOI: 10.4995/agt.25653
• Enlaces
  • Texto completo
• Resumen

  • Semitopological groups G and H are said to be HM-equivalent if the Hartman-Mycielski extensions G· and H· of G and H,respectively, are topologically isomorphic. It is shown that G and Gk are HM-equivalent, for every semitopological group G and an integer k ≥ 1 . We also show that if G and H are semitopological groups and G is topologically isomorphic to a subgroup of a finite power of H, then G·  admits a topological monomorphism to H· .

    It is established that the HM-equivalence relation preserves a variety of properties, especially those expressed in terms of cardinalfunctions. On the other hand, we show under some extra set-theoretic assumptions that the cellularity, Lindelöf property, countable compactness, tightness, Fréchet-Urysohn property, etc., are not preservedby the HM-equivalence in the class of topological groups.

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