9 Notations
| Notation | Description | Source |
| $\mathcal{N}_{X}(A)$, $\mathcal{N}(A)$, $\mathcal{N}^{o}(A)$ | Neighbourhood filter at $A$; open neighbourhoods of $A$. | Definition 5.4.1 |
| $C(X; Y)$ | Continuous functions $X \to Y$. | Definition 5.6.1 |
| $E(d, r)$ | $\{(x,y) \in X \times X \mid d(x,y) < r\}$ for pseudometric $d$. | Definition 6.3.3 |
| $B(x, r)$ | Open ball $\{y \in X \mid d(x,y) < r\}$ for pseudometric $d$. | Definition 6.3.3 |
| $B(A, \varepsilon)$ | $\varepsilon$-fattening $\{x \in X \mid d(x, A) < \varepsilon\}$ of $A$. | Definition 8.2.3 |
$UC(X; Y)$ | Uniformly continuous functions $X \to Y$. | Definition 6.2.1 |
| $U^{-1}$ | Inversion of $U \subset X \times X$. | Definition 6.1.1 |
| $U \circ V$ | Composition of $U, V \subset X \times X$. | Definition 6.1.2 |
| $U(A)$ | Slice of $U \subset X \times Y$ at $A \subset X$: $\{y \mid \exists x \in A,\, (x,y) \in U\}$. | Definition 6.1.3 |
| $E(S, U)$ | Entourage of the form $\{(f,g) \in X^{T} \mid (f(x),g(x)) \in U\ \forall x \in S\}$. | Definition 7.1.2 |
| $\mathfrak{E}(\mathfrak{S}, \mathfrak{U})$ | $\mathfrak{S}$-uniformity, generated by $\{E(S,U) \mid S \in \mathfrak{S},\ U \in \mathfrak{U}\}$. | Definition 7.1.2 |
$\mathrm{supp}(f)$ | Support of $f$. | Definition 5.19.1 |
| $C_{c}(X; E)$ | Compactly supported continuous functions $X \to E$. | Definition 5.19.2 |
| $f \prec U$ | $f \in C_{c}(X; [0,1])$ with $\mathrm{supp}(f) \subset U$. | Definition 5.19.3 |
| $C_{0}(X; E)$ | Continuous functions vanishing at infinity. | Definition 5.21.1 |
| $BC(X; E)$ | Bounded continuous functions $X \to E$. | Definition 10.11.3 |