Subset notation in Analysis

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I have been reading through the Han Lin book on elliptic PDEs and am confused with some of the notation they are using.

For one, they use $A\Subset B$ to mean $\overline{A}$ is a compact subset of B.

In the third chapter (pg 53), they use $\subset_+$ to denote what seems to be a proper subset.

Am I right on this?

Also, are there any resources that explain common notation in analysis? They don't explain any of the notation in the book, and since I don't have that much experience in this subject I am often left confused by what they mean.