Continuous posets

Abbreviation: ContPos

Definition

A \emph{continuous poset} is a structure A=A,A=A, of type such that

A,A, is a name of class

op1op1 is (name of property): axiom1axiom1

op2op2 is …:

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It is not unusual to give several (equivalent) definitions. Ideally, one of the definitions would give an irredundant axiomatization that does not refer to other classes.

Morphisms

Let AA and BB be … . A morphism from AA to BB is a function h:ABh:AB that is a homomorphism: h(xy)=h(x)h(y)h(xy)=h(x)h(y)

Definition

An \emph{…} is a structure A=A,A=A, of type such that

is …: axiomaxiom

is …: axiomaxiom

Examples

Example 1:

Basic results

Properties

Finite members

$\begin{array}{lr}

f(1)= &1\\
f(2)= &\\
f(3)= &\\
f(4)= &\\
f(5)= &\\

\end{array}\begin{array}{lr}

f(6)= &\\
f(7)= &\\
f(8)= &\\
f(9)= &\\
f(10)= &\\

\end{array}$

Subclasses

[[...]] subvariety
[[...]] expansion

Superclasses

[[...]] supervariety
[[...]] subreduct

References


1) F. Lastname, \emph{Title}, Journal, \textbf{1}, 23–45 MRreview

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