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:
“A masterpiece is ... something said once and for all, stated, finished, so that it’s there complete in the mind, if only at the back.”
—Virginia Woolf (1882–1941)