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We are studying topology. There are a lot of definitions and theorems. I wonder if there somewhere knowledge base about topology and reasoning system exists. So I expect some tool that systematizes all things in topology and can answer me some simple questions about properties of topological object, give me list of theorems for some topics ans so on.

My science interest is about IT and mathematical modeling. And i chose topology as extra course just for curiosity.

Nobody in my group knows about such tool. I mean some software tool as i know tables and diagrams for example in Engelking, General Topology.

Thanks a lot and sorry for English (it's not my native).

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    $\begingroup$ This seems likely to get closed, but before it does, I'd like to point out that a decent textbook accomplishes all of these except being software. Is there any reason why you feel a textbook is not sufficient to learn topology? $\endgroup$
    – Logan M
    Commented Mar 17, 2011 at 13:33
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    $\begingroup$ Also a book: Counterexamples in Topology (Steen and Seebach) has summaries and charts in the introductory chapter. $\endgroup$
    – Gerald Edgar
    Commented Mar 17, 2011 at 13:51
  • $\begingroup$ I think that topospaces.subwiki.org/wiki/Main_Page is made with similar intentions, but I would say there's a lot of work to be done. However, you can find some relations between various properties. Of course, it is a wiki, not an expert system. $\endgroup$
    – Martin Sleziak
    Commented Mar 17, 2011 at 17:49

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I was working on a project like this about five years ago, but I abandoned it. I entered the tables from Counterexamples in Topology that list the topological spaces and their properties, and I created a list of logical dependencies among the properties. I also wrote Python code to search for spaces having specified properties, and to test whether certain combinations of properties are logically consistent (using the Davis-Putnam algorithm).

Your post inspired me to dust this work off and share it, even though it's not fully baked yet. I have uploaded the data files to GitHub, and I will post my Python code as soon as I have cleaned it up. Contact me if you would like to participate in this project.

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  • $\begingroup$ I am watching it. Thanks. I am going to discuss it with our group on next Thursday (24.03.2011) $\endgroup$
    – mathemage
    Commented Mar 18, 2011 at 6:00

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