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, groups and/or spaces:
“Trees appeared in groups and singly, revolving coolly and blandly, displaying the latest fashions. The blue dampness of a ravine. A memory of love, disguised as a meadow. Wispy clouds—the greyhounds of heaven.”
—Vladimir Nabokov (1899–1977)
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Policemen so cherish their status as keepers of the peace and protectors of the public that they have occasionally been known to beat to death those citizens or groups who question that status.”
—David Mamet (b. 1947)
“Deep down, the US, with its space, its technological refinement, its bluff good conscience, even in those spaces which it opens up for simulation, is the only remaining primitive society.”
—Jean Baudrillard (b. 1929)