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I have two questions about the definition of topological semigroup. Thank you very much to all the respondents.

Q1. Why topological space has to be Hausdorff when defining topological semigroups?

Q2. If the topological space is not Hausdorff, can we not give a definition of the topological semigroup.

MBKandemir
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  • You can make the definition without, but it is usually made with in order to avoid pathologies. In topological group theory, eg, you want points to be closed and Hausdorffness is a cheap way to get there. – Randall Oct 09 '17 at 21:06
  • Thank you. Is there a source that makes the definition without the Hausdorffness? Is there one you would recommend to me. – MBKandemir Oct 09 '17 at 21:23
  • Maybe you are interested to add the tags (separation-axioms), (definition) and/or (general-topology). On the other hand, maybe you don't know that if you want to draw the attention of an user you need to prefix the nick of the user with the symbol @ (see different post if you've doubts). Isn't required a response of this comment. Good week. –  Oct 09 '17 at 21:45

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