On cofree S-spaces and cofree S-flows

• Khosravi, Behnam ^[1]
  1. [1] Institute for Advanced Studies in Basic Sciences
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 13, Nº. 1, 2012, págs. 1-10
• Idioma: inglés
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• Resumen

  • Let S-Tych be the category of Tychonoff S-spaces for a topological monoid S. We study the cofree S-spaces and cofree S-flows over topological spaces and we prove that for any topological space X and a topological monoid S, the function space C(S,X) with the compact-open topology and the action s · f = (t → f(st)) is the cofree S-space over X if and only if the compact-open topology is admissible and Tychonoff. Finally we study injective S-spaces and we characterize injective cofree S-spaces, when the compact-open topology is admissible and Tychonoff. As a consequence of this result, we characterize the cofree S-spaces and cofree S-flows, when S is a locally compact topological monoid.