Notations
=========

.. list-table::
   :header-rows: 1

   * - Notation
     - Description
   * - :math:`\partial{X}`
     - boundary of :math:`X` where :math:`X \subseteq \mathbb{R}^{2}`
   * - :math:`N_{\varepsilon}(x)`
     - open :math:`\varepsilon`-neighborhood of :math:`x` where :math:`x \in \mathbb{R}^{2}`
   * - :math:`N_{\varepsilon}(X)`
     - :math:`\bigcup_{x \in X} N_{\varepsilon}(x)` where :math:`X \subseteq \mathbb{R}^{2}`
   * - :math:`\sigma(\mathcal{X})`
     - index function defined as :math:`\sigma(\mathcal{X}) := n` where :math:`\mathcal{X} = \{X_{1}, \cdots, X_{n}\}`
   * - :math:`A(X)`
     - area of :math:`X` where :math:`X \subseteq \mathbb{R}^{2}`
   * - :math:`\overline{X}`
     - closure of :math:`X \subseteq \mathbb{R}^{2}`
   * - :math:`X^{\circ}`
     - interior of :math:`X \subseteq \mathbb{R}^{2}`
   * - :math:`X^{C}`
     - complement of :math:`X \subseteq \mathbb{R}^{2}`