What does this “subset” symbol mean?

Question

I just came across this "subset" symbol in a PDF:

$$\Omega \subsetneq T$$

I've never seen it before, and I tried looking for it via Detexify (to no avail). What does it mean?

Answer 1

This means $\Omega$ is a proper subset of $T$. That is, $\Omega\subseteq T$ but $\Omega \neq T$.

For example, $\{1, 2, 3\}\subsetneq \{1, 2, 3, 4\}$.

Answer 2

$\subsetneq$ ($\text{"\\subsetneq"}$) means: subset, but not equal.

Here's a nice example:

Let Ω be a half-strip in the complex plane: $$ \Omega = \{ z \in \mathbb{C} | x_1 \leq \mathrm{Re} (z) \leq x_2 \text{ and } \mathrm{Im} (z) \geq y_0 \} \subsetneq \mathbb{C}. \, $$