Complete Lattice: Total Order A totally ordered set (with its order topology) which is a complete lattice is compact. Examples are the closed intervals of real numbers, e.g. the unit interval [0,1], and the affinely extended real number system (extended real number line). There are order-preserving homeomorphisms between these examples.

Complete Lattice: Total Order
A totally ordered set (with its order topology) which is a complete lattice is compact. Examples are the closed intervals of real numbers, e.g. the unit interval [0,1], and the affinely extended real number system (extended real number line). There are order-preserving homeomorphisms between these examples.

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