order-preserving map

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order-preserving map

Order-preserving map from a poset $L$ to a poset $M$ is a function $f$ such that

\forall x,y\in L:(x\geq y\implies f(x)\geq 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\geq y\implies f(x)\leq f(y)).

Order-reversing maps are also called antitone functions.

Defines:

monotonicity

Keywords:

partial order

Synonym:

monotone function,monotonic function,order homomorphism,isotone function,isotonic function,order-preserving, isotone, isotonic,order-reversing,antitonic,antitone

Type of Math Object:

Definition

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Reference

Mathematics Subject Classification

06A06 no label found

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Order homomorphism

Permalink Submitted by porton on Wed, 01/16/2008 - 16:54

Order homomorphism is the same as order-preserving map?

If yes, I will add it as a synonym to the definition of order-preserving map.
--
Victor Porton - http://www.mathematics21.org
* Algebraic General Topology and Math Synthesis
* 21 Century Math Method (post axiomatic math logic)
* Category Theory - new concepts

Re: Order homomorphism

Permalink Submitted by CWoo on Wed, 01/16/2008 - 20:12

Yes, they are the same.

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order-preserving map

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order-preserving map

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Order homomorphism

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order-preserving map

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Order homomorphism

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