It may not be exactly what you want, but I played with https://github.com/luqui/topology-extras/blob/master/TopologyExtras/Topology.hs a few months ago, it may be a good basis to start with. (no pun intended)

On Thu, Aug 11, 2011 at 5:08 PM, Grigory Sarnitskiy <sargrigory@ya.ru> wrote:
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" <sargrigory@ya.ru>:
> Hello! I just wonder whether it is possible to have a typeclass for topological spaces?
>
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