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What properties do you need to define the average of two members of a set? Does this kind of space have a name?

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The question is not clear enough. I am not even sure whether it is a research-level question. Can we have an example of what you have in mind? – Andrej Bauer Sep 14 2011 at 18:06
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 I suspect they are hunting around for a concept something like ncatlab.org/nlab/show/convex+space – Sridhar Ramesh Sep 14 2011 at 18:18
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 I think this question might be more appropriate for math.stackexchange.com than for MathOverflow. I do have an answer that might be helpful for you; if you move your question to math.stackexchange.com, I will post my answer there. – Vectornaut Sep 14 2011 at 18:38
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 @Sridhar Ramesh: I think you pretty much nailed it! – Grönwall Sep 14 2011 at 19:07
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 Too bad the topic was closed because the question was put badly. The answe is mid-point algebras, also known as medial means. If you type these keywords into Google Scholar you will get plenty of pointers. – Andrej Bauer Sep 15 2011 at 6:26
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closed as off topic by Noah Snyder, André Henriques, quid, Ryan Budney, Simon Thomas Sep 15 2011 at 0:43

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