A variety over a field is complete when its map to is universally closed: after any base change, projection sends closed subsets to closed subsets. For a separated finite-type variety, this is equivalent to being proper. In the classical algebraically closed setting one may test projections for arbitrary varieties. Images of rational points over a non-algebraically-closed field must not replace geometric images.
"Complete variety" refers to a concept in the field of economics, particularly in the context of consumer choice and market analysis. It generally describes a situation in which a consumer has access to all possible varieties or types of a good or service. This allows consumers to choose products that best match their preferences and needs. In a market with complete variety, consumers can find differing attributes (such as size, color, quality, and brand) in products, offering them a comprehensive selection to meet diverse preferences.
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