
18 Feb
2010
18 Feb
'10
3:47 p.m.
On 18 Feb 2010, at 20:20, Daniel Fischer wrote:
+ definition backtracking: «A closure operation c is defined by the property c(c(x)) = c(x).
Actually, that's incomplete, ...
That's right, it is just the idempotency relation.
...missing are - c(x) contains x - c(x) is minimal among the sets containing x with y = c(y).
It suffices*) with a lattice L with relation <= (inclusion in the case of sets) satifying i. x <= y implies c(x) <= c(y) ii. x <= c(x) for all x in L. iii. c(c(x)) = x. Hans *) The definition in a book on lattice theory by Balbes & Dwinger.