In 4-D flat metric E&M context, given a rank $p$ tensor, one can construct dual of $4-p$ rank tensor by Levi-Civita tensor. Here dual is not in the same sense of mathematical dual. I do not know where it comes from. The followings are my questions:
Is it necessarily true for arbitrary dimension that $n$, given a rank $p$ tensor, one always can have a rank $n-p$ tensor constructed by Levi-Civita tensor dual to the rank $p$ tensor?
If it is true, in any dimensional space+1 dimension time, any tensor and its dual contain the same information. Shouldn't the bigger the space, the more information be thrown in? Why am I expect this duality is true up to any dimension?
It seems somehow there is some sort of one to one correspondence between dual and double dual itself where dual is still not the familiar mathematical dual. I knew in math double dual space isomorphic to dual space which is different from what we are talking here. What is the correspondence in the E&M dual context?