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)
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