[Haskell-cafe] Category Theory woes

[Alexander Solla]

On Feb 18, 2010, at 10:19 AM, Nick Rudnick wrote:

> Back to the case of open/closed, given we have an idea about sets --  
> we in most cases are able to derive the concept of two disjunct sets  
> facing each other ourselves, don't we? The only lore missing is just  
> a Bool: Which term fits which idea? With a reliable terminology  
> using «bordered/unbordered», there is no ambiguity, and we can pass  
> on reading, without any additional effort.


There are sets that only partially contain their boundary.  They are  
neither open nor closed, in the usual topology.  Consider (0,1] in the  
Real number line.  It contains 1, a boundary point.  It does not  
contain 0.  It is not an open set OR a closed set in the usual  
topology for R.