[Haskell-cafe] Category Theory woes
Hans Aberg
haberg at math.su.se
Thu Feb 18 09:32:05 EST 2010
On 18 Feb 2010, at 14:48, Nick Rudnick wrote:
> * the definition of open/closed sets in topology with the boundary
> elements of a closed set to considerable extent regardable as facing
> to an «outside» (so that reversing these terms could even appear
> more intuitive, or «bordered» instead of closed and «unbordered»
> instead of open),
I take "closed" as coming from being closed under limit operations -
the origin from analysis. A closure operation c is defined by the
property c(c(x)) = c(x). If one takes c(X) = the set of limit points
of X, then it is the smallest closed set under this operation. The
closed sets X are those that satisfy c(X) = X. Naming the complements
of the closed sets open might have been introduced as an opposite of
closed.
Hans
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