\chapter{Notations}
\label{chap:topology-notations}

\begin{tabular}{lll}
    \textbf{Notation} & \textbf{Description} & \textbf{Source} \\
    \hline
    % ---- General Topology ----
    $\mathcal{N}_X(A)$, $\mathcal{N}(A)$, $\mathcal{N}^o(A)$ & Neighbourhood filter at $A$; open neighbourhoods of $A$. & \autoref{definition:neighbourhood} \\
    $C(X; Y)$ & Continuous functions $X \to Y$. & \autoref{definition:continuity} \\
    $E(d, r)$ & $\{(x,y) \in X \times X \mid d(x,y) < r\}$ for pseudometric $d$. & \autoref{definition:pseudometric-uniformity} \\
    $B(x, r)$ & Open ball $\{y \in X \mid d(x,y) < r\}$ for pseudometric $d$. & \autoref{definition:pseudometric-uniformity} \\
    $B(A, \varepsilon)$ & $\varepsilon$-fattening $\{x \in X \mid d(x, A) < \varepsilon\}$ of $A$. & \autoref{definition:fattening} \\

    % Uniform Spaces
    $UC(X; Y)$ & Uniformly continuous functions $X \to Y$. & \autoref{definition:uniformcontinuity} \\
    $U^{-1}$ & Inversion of $U \subset X \times X$. & \autoref{definition:inversion} \\
    $U \circ V$ & Composition of $U, V \subset X \times X$. & \autoref{definition:composition} \\
    $U(A)$ & Slice of $U \subset X \times Y$ at $A \subset X$: $\{y \mid \exists x \in A,\, (x,y) \in U\}$. & \autoref{definition:slice} \\
    $E(S, U)$ & Entourage of the form $\{(f,g) \in X^T \mid (f(x),g(x)) \in U\ \forall x \in S\}$. & \autoref{definition:set-uniform} \\
    $\mathfrak{E}(\sigma, \mathfrak{U})$ & $\sigma$-uniformity, generated by $\{E(S,U) \mid S \in \sigma,\ U \in \mathfrak{U}\}$. & \autoref{definition:set-uniform} \\

    % Function Spaces
    $\mathrm{supp}(f)$ & Support of $f$. & \autoref{definition:support} \\
    $C_c(X; E)$ & Compactly supported continuous functions $X \to E$. & \autoref{definition:compactly-supported} \\
    $C_c^+(X)$ & Compactly supported continuous functions $X \to [0, \infty)$ & \autoref{definition:non-negative-compactly-supported}
    $f \prec U$ & $f \in C_c(X; [0,1])$ with $\mathrm{supp}(f) \subset U$. & \autoref{definition:compactly-supported-01} \\
    $C_0(X; E)$ & Continuous functions vanishing at infinity. & \autoref{definition:vanish-at-infinity} \\
    $BC(X; E)$ & Bounded continuous functions $X \to E$. & \autoref{definition:bounded-continuous-function-space} \\
\end{tabular}