Appropriate symbol to denote feasible region

Question

I have an optimization problem such as $$ \min_{x\in\mathop{Range}(\mathbf A) \text{ s.t. } \mathbf B x = b} \|x\| $$ which I would like to write more concisely as $$ \min_{x\in\mathcal{X}} \|x\| $$ where $\mathcal{X} = \{x \in \mathrm{Range}(A) : \mathbf{B}x = b\}$.

What symbol is traditionally used in place of $\mathcal{X}$ to denote the set of feasible $x$?

If the answer depends on whether the constraint set is linear or nonlinear, I am interested in both cases.

Answer 1

Step two¹ in "how to do a math problem": label the parts of the problem. So give the set you want a name.

"Let $S = \{x \in \mathrm{Range}(A) : \mathbf{B}x = b\}$. ... $$ \min_{x \in S} ||x|| $$ ... "

^{1 : The number of this step in any particular "how to do a math problem" may vary.}