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Π-Base – A community database of topological examples (jdabbs.com)
53 points by colinprince on Sept 15, 2015 | hide | past | web | favorite | 7 comments



Author checking in. There hasn't been much user-facing progress on this lately, but a colleague is currently working on a project to expand the scope and content, and I've been tinkering on integrating with Coq (as time permits (which is too infrequently)).

If you're interested in staying abreast, sign up for the newsletter (http://jdabbs.us9.list-manage2.com/subscribe?u=f81a0c2648f40...). If you're interested in getting involved, let me know (https://twitter.com/jamesdabbs).


HN news title currently using a captial Pi sign, aka П, which is the same as the letter for "Pe" in many Cyrillic scripts. In fact, the Cyrillic letter itself comes from the Greek symbol for Pi.

https://en.wikipedia.org/wiki/Pe_(Cyrillic)


I was thinking about such think since reading Engelking's introduction to topology. (When dealing with topology, it's so natural to think about both implications, and examples of spaces (or, as importantly, counterexamples).)


Can someone explain the purpose of this database? The page doesn't give any hints.

(I get it's math-related, but what is it useful for?)


The motivating use case is: I'm doing some topology research, and exploring a new property P. I've determined how it relates to some well-studied properties A,B and C (say A => P, P => B, and P => not C). I'd like a list of example spaces that I can examine where P is interesting (spaces satisfying B, not C and not A in this case). In general the hope is to streamline what is currently a pretty tedious literature search, and to encourage researchers to better pool their knowledge.

The other main use case now is educational - I definitely would have liked a site like this when I was taking my intro to topology class and grappling with examples to get my head 'round things, and I know of a seminar that ran using the db as a hook to get students being self-directed, exploring, and contributing more than undergrad mathematics usually allows.

Admittedly, that may not seem "useful" unless you're a topologist.


It looks similar to the OEIS (Online Encyclopedia of Integer Sequences). Any time a problem comes up whose solution involves topology, this is a good place to go and avoid re-discovering a space that might already be known and well studied.


Saving this link. Looks great at first glance.




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