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Topology Gossip

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Brubeck is a database of topological information, à la the classic Counterexamples in Topology. It contains descriptions of several important topological spaces and properties and the interrelationships between each of them.

This is quite interesting. Brubeck, by James Dabbs, is a bit like Number Gossip but for topological spaces: it presents you with a search box into which you can type a list of properties you want a topology to have or not have, and it returns a list of matches. It also automatically geenerates proofs (really simple implication trees) based on theorems it’s been told and the facts it is given about spaces, and displays its working-out graphically.

Site: Brubeck

Source: /r/math

All metro systems eventually have the same shape

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The BBC and Scientific American report on a paper looking, “in an exploratory manner,” at the limiting shape of metro systems serving large cities. The BBC linked to the actual paper, which is nice of them. The Scientific American article goes into a bit more detail, though.

The authors contend that rather than the shape of subway networks being decided by central planning, which would produce a variety of shapes, the eventual shape of a subway network converges on an emergen structure consisting of a dense core with branches radiating from it.

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