Oh, I guess the class would look something like that: class TopologicalSpace a where ifOpen :: (Subset a) -> Bool and Subset x is a type corresponding to subsets of x. 11.08.2011, 17:52, "Grigory Sarnitskiy" :

Hello! I just wonder whether it is possible to have a typeclass for topological spaces?

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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 wrote:

Hello! I just wonder whether it is possible to have a typeclass for topological spaces?

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