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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