Re: set inclusion notation in Capinski & Kopp ambiguous

I have seen both notational conventions used.

I think $A \subset B$ used to be generally accepted as meaning $a \in A 
\implies a \in B$. This does not preclude $A = B$. I think this because 
the notation was popular with older professors. Now people seem to assume 
it has the extra meaning that there exists $b \in B$  such that $b \not 
\in A$.

Mathematics has no governing body which regulates notation, so people 
tend to adopt their own conventions based on their own education.

There is no problem with this but as you point out it is ambiguous. It is 
also a criminal crime to mix two notational conventions. I can well 
believe that this is the case in the book you are currently reading. I 
can't remember ever reading a maths book without wanting to kick the 
author(s) repeatedly on a regular basis. 

Brian