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A poset is totally ordered if

A poset is totally ordered if. A totally ordered poset is called a chain. The set. with the relation. Let be the set of all real numbers, and let have the usual meaning; then is a chain. if for all.

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A poset is totally ordered if

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  1. A poset is totally ordered if A totally ordered poset is called a chain.

  2. The set with the relation • Let be the set of all real numbers, and let have the • usual meaning; then is a chain. if for all is a poset. It is a chain if and only if d = 1. • Given a set E, the power set Ρ(E) comprising all subsets of E • becomes a poset under the inclusion relation, that is, if and only if The empty set is denoted by Examples:

  3. Let be the set of all nonnegative integers, and put if m divides n. Then is a poset.

  4. Inclusion relation and Hasse diagrams

  5. or

  6. is a segment (a subset of a partition) of X containing p and

  7. The connected component labelling

  8. Sequential algorithm Initially: lbl (label image)  0; lval (current label)  0; t is the current flat zone

  9. City-block metric: • Chessboard metric • Euclidean distance

  10. Distance functions

  11. = backward 4- or 8-connected neighbors = forward 4- or 8-connected neighbors

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