On 18 Feb 2010, at 19:19, Nick Rudnick wrote:
agreed, but, in my eyes, you directly point to the problem:
* doesn't this just delegate the problem to the topic of limit
operations, i.e., in how far is the term «closed» here more
perspicuous?
* that's (for a very simple concept) the way that maths prescribes:
+ historical background: «I take "closed" as coming from being
closed under limit operations - the origin from analysis.»
+ definition backtracking: «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.»
418 bytes in my file system... how many in my brain...? Is it
efficient, inevitable?
Yes, it is efficient conceptually. The idea of closed sets let to
topology, and in combination with abstractions of differential
geometry led to cohomology theory which needed category theory solving
problems in number theory, used in a computer language called Haskell
using a feature called Currying, named after a logician and
mathematician, though only one person.
Hans
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