You may want to, instead, check out the methods of point-free topology
(also known as pointless topology) where you, basically, study
topological spaces in terms of their open-set lattices.
This allows you to use a more algebraic language which probably fits
better into Haskell (I think this is used, for example, when studying
topology within type theories). A search for stone-duality should give
you somewhere to start (I know there are a sequence of posts on
http://topologicalmusings.wordpress.com/ on the subject).
Somewhat less known is the theory of formal topology (see for example
n-lab http://ncatlab.org/nlab/show/formal+topology). Which might also
be an approach to doing some topology in Haskell.
Hope that's of some help :)
On 11/08/2011, Grigory Sarnitskiy
Hello! I just wonder whether it is possible to have a typeclass for topological spaces?
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