On cofree S-spaces and cofree S-flows

Authors

  • Behnam Khosravi Institute for Advanced Studies in Basic Sciences

DOI:

https://doi.org/10.4995/agt.2012.1632

Keywords:

S-space, S-flow, Cofree S-space, Cofree S-flow Compact-open topology, Injective S-space

Abstract

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.

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Author Biography

Behnam Khosravi, Institute for Advanced Studies in Basic Sciences

Department of Mathematics, Institute for Advanced Studies in Basic Sciences,Zanjan 45137-66731, Iran

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Published

2012-04-15

How to Cite

[1]
B. Khosravi, “On cofree S-spaces and cofree S-flows”, Appl. Gen. Topol., vol. 13, no. 1, pp. 1–10, Apr. 2012.

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