[Haskell-cafe] Category Theory woes

[Hans Aberg]

On 18 Feb 2010, at 14:48, Nick Rudnick wrote:

> * the definition of open/closed sets in topology with the boundary  
> elements of a closed set to considerable extent regardable as facing  
> to an «outside» (so that reversing these terms could even appear  
> more intuitive, or «bordered» instead of closed and «unbordered»  
> instead of open),

I take "closed" as coming from being closed under limit operations -  
the origin from analysis. A closure operation c is defined by the  
property c(c(x)) = c(x). If one takes c(X) = the set of limit points  
of X, then it is the smallest closed set under this operation. The  
closed sets X are those that satisfy c(X) = X. Naming the complements  
of the closed sets open might have been introduced as an opposite of  
closed.

   Hans