I have always wondered why are the following concepts/objects in Mathematics named so :
3.) Exterior derivative (in differential geometry)
4.) Interior multiplication (in differential geometry).
5.) 'Soft' & 'Fine' sheaves
Some of these words (like the first two) have a common English usage and I can't see a relation between the common usage and the Mathematical usage so I assume that perhaps there is no connection but am not sure. And I do not understand what is exterior about exterior derivative or what is interior about interior multiplication in differential geometry. Any information about the history of this nomenclature will be helpful. Please feel free to add more words/terms to this list which raise a similar question.