[Haskell-cafe] Category Theory woes

Nick Rudnick joerg.rudnick at t-online.de
Thu Feb 18 17:08:16 EST 2010

Hi Alexander,

my actual posting was about rename refactoring category theory; 
closed/open was just presented as an example for suboptimal terminology 
in maths. But of course, bordered/unbordered would be extended by e.g. 
«partially bordered» and the same holds.



Alexander Solla wrote:
> 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.

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