from The American Heritage® Dictionary of the English Language, 4th Edition
- n. Mathematics A function that is onto.
from Wiktionary, Creative Commons Attribution/Share-Alike License
- n. A function of "many-to-one" mapping relationship; more formally, f: X → Y is a surjection if and only if, for every y in the codomain Y, there is at least one x in the domain X with f(x) = y.
'' 'surjection' '' is a [[function (mathematics) | function]] for which every possible output value occurs for one or more input values: that is, its image is the whole of its codomain.
It is easy to check that this function satisfies the relation, which has to be a surjection since the sequence is strictly increasing..
But the Zariski topology is not metrizable … is a surjection of sheaves (exercise!), yet the map on global sections is not surjective.
If you think about it, Arrays and Maps share the same underlying formalism (a surjection, not to put too fine a point on it), and in some languages, notably PHP, there isn't a user-visible difference between them.