Groups and Vector Spaces
If the component sets are ordered groups then the result is a non-Archimedean group, because e.g. n(0,1) < (1,0) for all n.
If the component sets are ordered vector spaces over R (in particular just R), then the result is also an ordered vector space.
Read more about this topic: Lexicographical Order
Famous quotes containing the words groups and/or spaces:
“Instead of seeing society as a collection of clearly defined “interest groups,” society must be reconceptualized as a complex network of groups of interacting individuals whose membership and communication patterns are seldom confined to one such group alone.”
—Diana Crane (b. 1933)
“Le silence éternel de ces espaces infinis m’effraie. The eternal silence of these infinite spaces frightens me.”
—Blaise Pascal (1623–1662)