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I have to admit I'm not really sure here. I've see the term "mapping" used that way in some Category theory articles, but that's about it. So if anyone feels he or she has a better overview of the usage of the word, please be bold ... -- JanHidders

The article on categories uses the word "map" rather than "mapping", by the way. "Map" is synonymous with "1-1 function" in Patrick Suppes: Introduction to Axiomatic Set Theory (1960). The Swedish National Encyclopedia (written from scratch and published 1989 - 1996) says that (the Swedish equivalents of) the three words "mapping", "function" and "transformation" are synonymous. -OJarnef