A place in the hall of fame and thank you for mentioning clopen... ;-)
Just wanting to present open/closed as and example of improvable maths
terminology, I oversaw this even more evident defect in it and even
copied it into my improvement proposal, bordered/unbordered:
It is questionable style to name two properties, if they can occur
combined, as an antagonistic pair...!
Acccordingly, it is more elegant to draw such terms from independent
domains.
This subject seems to drive me crazy... I actually pondered on
improvement, and came to:
«faceless» in replacement of «open»
Rough explanation: The «limit» of a closed set can by the limit of
another closed set that may even share only this limit -- a faceless set
has -- under the given perspective -- no such part to «face» to beyond.
Any comments?
But the big question is now: What (non antagonistic) name can be found
for the other property??
Any ideas...??
Cheers,
Nick
Ergonomic terminology comes not for free, giving a quick answer here
would be «maths style» with replacing
Michael Matsko wrote:
Nick,
Actually, clopen is a set that is both closed and open. Not one
that is neither. Except in the case of half-open intervals, I can't
remember talking much in topology about sets with a partial boundary.
Alexander Solla wrote:
Clopen means a set is both closed and open, not that it's "partially
bordered".
Daniel Fischer wrote:
And we'd be very wrong. There are sets which are simultaneously open and
closed. It is bad enough with the terminology as is, throwing in the
boundary (which is an even more difficult concept than open/closed) would
only make things worse.
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