Dilation On Complete Lattices
Complete lattices are partially ordered sets, where every subset has an infimum and a supremum. In particular, it contains a least element and a greatest element (also denoted "universe").
Let be a complete lattice, with infimum and minimum symbolized by and, respectively. Its universe and least element are symbolized by U and, respectively. Moreover, let be a collection of elements from L.
A dilation is any operator that distributes over the supremum, and preserves the least element. I.e.:
- ,
- .
Read more about this topic: Dilation (morphology)
Famous quotes containing the word complete:
“For which of you, intending to build a tower, does not first sit down and estimate the cost, to see whether he has enough to complete it?”
—Bible: New Testament, Luke 14:28.