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May 5, 2026Applied General Topology2 citationsOpen Access

Ti-reflections and the Hartman–Mycielski construction in semitopological and paratopological groups

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BRBoris Reyes

Key Points

  • The aim is to explore the relationships between different constructions of semitopological and paratopological groups.
  • Analyzed isomorphisms between semitopological groups Ti(G∙) and (Ti(G))· for each index i.
  • Investigated the isomorphic properties of paratopological groups Reg(G·) and (Reg(G))·.
  • The semitopological groups Ti (G∙) and (Ti(G))· are shown to be topologically isomorphic.
  • The paratopological groups Reg(G·) and (Reg(G))· are confirmed to be topologically isomorphic.

Abstract

We show that, given a semitopological group G, the semitopological groups Ti (G∙) and (Ti (G) ) ·, for each i ∈ 0, 1, 2, and (Gsr) · and (G·) sr, are topologically isomorphic. Moreover, we prove that, given a paratopological group G, the paratopological groups Reg (G·) and (Reg (G) ) · are topologically isomorphic.

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Cite This Study

Boris Reyes (2026) studied this question.

synapsesocial.com/papers/69f9886315588823dae17629https://doi.org/10.4995/agt.24809
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