Index of notation

The reference numbers indicate the chapter, section and subsection or exercise, in that order.

$T$ : V, 1, 2. $a^x$ (a any real number > 0, x any real number) : V, 4, 1. $\log_a x$ (a, x real numbers > 0, $a \neq 1$) : V, 4, 1. $\mathbf{R}^n$ : VI, 1, 1. $d(x, y)$ (Euclidean distance) : VI, 2, 1. $\|x\|$ (Euclidean norm) : VI, 2, 1. $(x|y)$ (scalar product) : VI, 2, 2. $S_n, B_n, R_n^*$ : VI, 2, 3. $P_n(\mathbf{R}), P_n$ : VI, 3, 1. $\tilde{\mathbf{R}}$ : VI, 3, 3. $\infty$ (point of $\tilde{\mathbf{R}}$) : VI, 3, 3. $P_{n,p}(\mathbf{R}), P_{n,p}$ : VI, 3, 5. $r(G), d(G)$ (G any closed subgroup of $\mathbf{R}^n$) : VII, 1, 2. $G^*$ (G any subgroup of $\mathbf{R}^n$) : VII, 1, 3. $T^n$ : VII, 1, 4. $C, i$ : VIII, 1, 1. $\Re(z), \Im(z), \overline{z}, |z|$ (z a complex number) : VIII, 1, 1. $C*, U$ : VIII, 1, 3. $H$ : VIII, 1, 4. $e(x)$ ($= e^{2\pi ix}$) : VIII, 2, 1. $(\Delta_1, \Delta_2)$ ($\Delta_1, \Delta_2$ rays) : VIII, 2, 2. $\partial, \omega$ : VIII, 2, 2. $Am (z)$ (z a complex number) : VIII, 2, 2. cos $\theta$, sin $\theta$, tan $\theta$ ($\theta$ an angle) : VIII, 2, 2. $\cos_a x, \sin_a x, \tan_a x, \cot_a x$ (x a real number) : VIII, 2, 4. cos $x$, sin $x$, tan $x$, cot $x$ (x a real number) : VIII, 2, 4. $(\widehat{D_1}, \widehat{D_2})$ (D_1, D_2 lines) : VIII, 2, 6. $\delta_0$ : VIII, 2, 6. $C^n$ : VIII, 4, 1. $P_n(C), \tilde{C}$ : VIII, 4, 3.

∞ (point of $\tilde{C}$) : VIII, 4, 3. $P_{n,p}(C)$ : VIII, 4, 4. $\beta X$ (X a completely regular space) : IX, 1, Exercise 7. $d(A, B), d(x, A)$ [x a point, A, B subsets of a metric space in which the distance between two points is denoted by $d(x, y)$] : IX, 2, 2 $|x|$ (absolute value in a valued division ring) : IX, 3, 2. $||x||$ (norm in a normed space) : IX, 3, 3. $D(A)$ : IX, 5, Exercise 3. $L(C)$ (C a sieve) : IX, 6, 5. $\prod_{n \in \mathbf{N}} x_n$ : IX, Appendix, 1. $\prod_{n=h}^{\infty} x_n$ : IX, Appendix, 3. $\prod_{n=0}^{\infty} x_n$ : IX, Appendix, 3. $\mathscr{F}(X; Y), H(x)$ [H a subset of $\mathscr{F}(X; Y)$], $\Phi(x)$ [$\Phi$ a filter on $\mathscr{F}(X; Y)$], $u|A, H|A$ [A a subset of X, $u \in \mathscr{F}(X; Y), H \subset \mathscr{F}(X; Y)$] : X, 1. $W(V)$ (V an entourage of Y) : X, 1, 1. $\mathscr{F}_u(X; Y)$ : X, 1, 1. $\mathscr{F}_{\mathscr{G}}(X; Y)$ : X, 1, 2. W(A, V) (A $\in \mathscr{G}$, V an entourage of Y) : X, 1, 2. $\mathscr{F}_s(X; Y), \mathscr{F}_c(X; Y)$ : X, 1, 3. $\mathscr{C}(X; Y), \mathscr{C}_{\mathscr{G}}(X; Y), \mathscr{C}_s(X; Y), \mathscr{C}_c(X; Y), \mathscr{C}_u(X; Y)$ : X, 1, 6. $\mathscr{C}_{\mathscr{G}}(X; Y)$ : X, 1, 6. $\tilde{x}$ (x a point of X) : X, 2, 1. $\mathscr{B}_{\mathscr{G}}(X; Y), \mathscr{B}(X; Y)$ (Y a metric space) : X, 3, 1. $||u||$ (u a bounded mapping into a normed space) : X, 3, 2. $\mathscr{L}(X_1, \ldots, X_n; Y)$ ($X_1, \ldots, X_n$ and Y being normed spaces) : X, 3, 2. $||u||_i$ (u a multilinear mapping of a product of normed spaces into a normed space) : X, 3, 2. $T(K, U)$ (K a compact subset of X, U an open subset of Y) : X, 3, 4. $\mathscr{C}_{\beta}$ : X, 3, 5. $C^{\infty}(X; \mathbf{R})$ : X, 4, Exercise 6 $vX$ : X, 4, Exercise 17.