It looks like a lower-case epsilon, but the Wikipedia page on epsilon states that they are not the same.
Does this symbol have a typographic identification outside of mathematics? Where did the symbol come from?
[Math] the name of the $\in$ symbol and where does it come from
elementary-set-theorymath-historynotation
Related Solutions
It is the interior product (Wikipedia page, MathWorld page). It's defined on page 334-336 of Lee's book:
The textbook is not making typos. The symbol $\subset$ is called a proper subset. For example, $$[0,1] \subset [0,2],$$ but $$[0,2] \not\subset [0,2].$$
However, the symbol $\subseteq$ means that a set can be contained in itself as well, for example, $$[0,1] \subseteq [0,2]$$ and $$[0,2] \subseteq [0,2].$$
This page describes a little more on the difference between subset and proper subset.
Best Answer
This is the membership relation, but in set theory this is also known as the epsilon relation, and historically the notation was indeed $\varepsilon$.
(For example, I have the book from 1948 by Tarski and Jonsson Cardinal Algebras where such notation is employed.)
According to this page it was Peano who used epsilon. I suppose somewhere around the 1960's or so, when typography was easier to modify the symbol was taking the modern shape of $\in$ (Bourbaki in their set theory book, ca. 1970, were using $\in$).