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.
Cheers,
Nick
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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