Erosions 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.
An erosion in is any operator that distributes over the infimum, and preserves the universe. I.e.:
- ,
- .
Read more about this topic: Erosion (morphology)
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“Man finds nothing so intolerable as to be in a state of complete rest, without passions, without occupation, without diversion, without effort. Then he feels his nullity, loneliness, inadequacy, dependence, helplessness, emptiness.”
—Blaise Pascal (1623–1662)