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Hi,
I am making a website to help students explore questions in point-set
topology.
http://topology.tinyclouds.org/
The website has a database which stores theorems and a logical deducer
which can figure out new theorems from the ones already entered. For
example, the theorem every Hausdorff is a T_0 space can be infered from
the two theorems Hausdorff implies T1 and T1 implies T0. The website
can generate a proof for this:
topology.tinyclouds.org/clause/not_hausdorff/t0">http://topology.tinyclouds.org/clause/not_hausdorff/t0
Also, the website has a database of actual spaces too. The website can
use these to give counter examples to false theorems. For example, here
is a space called the Tychonoff Corkscrew:
topology.tinyclouds.org/spaces/show/8">http://topology.tinyclouds.org/spaces/show/8
People who log into the website can edit / add / and delete the
information in the database. The goal is to have a complete repository
(or more complete) of all point-set topology facts.
This software is under development, and there are many bugs in the
website, but the software is open source. I encourage any one
interested in the site to contact me so that we can share ideas.
Thanks,
Ryan Dahl
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