The symbol $\Subset$ (occurring in places where $\subseteq$ could occur syntactically) comes up frequently in a paper I'm reading. The paper lives at the intersection of a few areas of math, and I don't even know where to begin looking for the meaning of a symbol whose latex code is "\Subset". Do you know what this usually denotes?

Edit: some context follows.

All the sets in question are subsets of $\hat{\mathbb{C}} = \mathbb{C}\cup\{\infty\}$.

Example 1. In a situation where $J$ is closed with empty interior, $U$ and $V$ are closed with $U\subsetneq V$, it is written "Note that $J \Subset U$ and, selecting a neighborhood $W \subset U$ of $J$ which is compactly contained in $V$, ..."

Example 2. In a situation where $R$ is a rational mapping, and where it is assumed that $B\subset \hat{\mathbb{C}}$ is such that $R(B)\Subset B$, it is written "Let $\Omega_0 = \hat{\mathbb{C}}\setminus B$. Define $\Omega_1 = R^{-1}(\Omega_0)$. By the properties of $B$, we have $\Omega_1\Subset\Omega_0$. If we let $U_0$ be any finite union of closed balls such that $\Omega_1 \subset U_0 \subset \Omega_0$, ..."

In both cases I have paraphrased to simplify the notation, so I hope I have not introduced errors into it.