The Hartman-Mycielski construction and topological monomorphisms
Abstract
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.
Fields of Study & Subjects
Advanced Topology and Set Theory
Computability
Logic
AI Algorithms
Advanced Algebra and Logic
Publication details
- Journal / source
- Applied General Topology
- Publisher
- Universitat Politecnica de Valencia
- Volume
- 27
- Issue
- 2
- Pages
- 25653–25653
- Publication date
- 23 June 2026
- Language
- EN