Dense linear orders

Definition

A dense linear order is a chain D = (D, ≤ ) such that  ≤  is dense:   x < y  ⇒  ∃z (x < z  and  z < y) where x < y  ⇔   x ≤ y  and  x ≠ y.

Remark:

Morphisms

Let C and D be dense linear orders. A morphism from C to D is a function h : C→D that is a orderpreserving: x ≤ y  ⇒  h(x) ≤ h(y).

Some results

Examples

Properties

Finite members

Subclasses

Superclasses