[Haskell-cafe] [Ann] group-theory

[Olaf Klinke]

Koji Miyazato wrote:
> > You can use `MonoidNull`. from monoid-subclasses to avoid an `Eq`
> constraint.
> 
> For groups, there is no difference between `MonoidNull` and `Eq`, as
> you can define `x == y` be
> `null (x <> inv y)`. There are monoids which `==` is not even
> decidable but `null` is (e.g. context-free grammars
> with equality defined by the language it defines), but such monoid
> necessarily has no `Group` instance.

A beautiful example of topological groups: Their topology is completely
determined by the neighbourhoods of the identity element. If the
identity element is isolated, the entire group is discrete. 

Olaf