I just begin to study math books in English but I am not a native speaker. I am confused about the following mathematical terms:
function(s), mapping(s), operator(s), projection(s)
Is there anyone can explain in details about the similarities and differences between these terms, and what mathematicians want to emphasize when they use them?
PS. I think they are very similar and sometimes interchangeable to each other, because they all imply some relations pairing from one set to another set. Briefly speaking, in my opinion, mapping just means a connection, function is a specific mapping from input set to output set but the output object is restricted to be unique, operator is a specific mapping from space to space (while space is a specific set?), projection sounds like mapping. In summary, function $\subset$ functional $\subset$ operator $\subset$ mapping $\equiv$ projection, OR functional $\subset$ operator $\subset$ function $\subset$ mapping $\equiv$ projection?