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order-preserving map
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(Definition)
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Order-preserving map from a poset $L$ to a poset $M$ is a function $f$ such that $$\forall x,y\in L:(x\ge y\implies f(x)\ge f(y)).$$
Order-preserving maps are also called monotone functions or monotonic functions or order homomorphisms or isotone functions or isotonic functions.
Order-reversing map from a poset $L$ to a poset $M$ is a function $f$ such that $$\forall x,y\in L:(x\ge y\implies f(x)\le f(y)).$$
Order-reversing maps are also called antitone functions.
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"order-preserving map" is owned by porton.
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See Also: poset, lattice homomorphism
| Other names: |
monotone function, monotonic function, order homomorphism, isotone function, isotonic function, order-preserving, isotone, isotonic, order-reversing, antitonic, antitone |
| Also defines: |
monotonicity |
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Cross-references: map, function, poset
There are 46 references to this entry.
This is version 7 of order-preserving map, born on 2008-01-16, modified 2009-10-05.
Object id is 10195, canonical name is OrderPreservingMap.
Accessed 4631 times total.
Classification:
| AMS MSC: | 06A06 (Order, lattices, ordered algebraic structures :: Ordered sets :: Partial order, general) |
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Pending Errata and Addenda
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