Index of notation

The reference numbers indicate the chapter, section and sub-section (or, exercise) in that order.

$\mathring{A}, \overline{A}$ (A a subset of a topological space) : I, 1, 6. $\varprojlim X_\alpha$ [$(X_\alpha)$ an inverse system of topological spaces] : I, 4, 4. $\tilde{f}(a)$ ($\tilde{f}$ the germ of a mapping) : I, 6, 10. $\lim_{x,\mathfrak{F}} f, \lim_{x} f(x), \lim_{x} f(x)$ : I, 7, 3. $\lim_{n \to \infty} x_n$ : I, 7, 3. $\lim_{x \in A} f(x)$ (A a directed set) : I, 7, 3. $\lim_{x \geq a} f(x)$ : I, 7, 4. $\lim_{x \geq a, x \in A} f(x), \lim_{x \geq a, x \neq a} f(x)$ : I, 7, 5. $f_T$ : I, 5, 1. $t_X$ : I, 10. $Fr (A)$ (A a subset of a topological space) : I, 1, Exercise 5. $\mathfrak{T}_0(X), \mathfrak{T}_+(X), \mathfrak{T}_-(X)$ : I, 2, Exercise 5. $\mathfrak{B}_0(X), \mathfrak{T}_\Omega, \mathfrak{T}_\Phi$ : I, 2, Exercise 7. $\mathfrak{F}(X), \mathfrak{T}_\Theta$ : I, 8, Exercise 12. $\mathfrak{T}^*$ : I, 8, Exercise 20. $\mathfrak{K}(X)$ : I, 9, Exercise 13. $\varprojlim X_\alpha$ [$(X_\alpha)$ an inverse system of uniform spaces] : II, 2, 7. $\hat{X}$ (the Hausdorff completion of a uniform space X) : II, 3, 7. $\tilde{\mathfrak{U}}, \mathfrak{T}(\tilde{\mathfrak{U}})$ : II, 1, Exercise 5. $X/G$ (G a group operating on a space X) : III, 2, 4.

$P(K, L)$ (K, L subsets of a space with operators) : III, 4, 5.

$\sum_{i \in I} x_i, \sum_i x_i, \sum x_i :$ III, 5, 1.

$\prod_{i \in I} x_i, \prod_i x_i, \prod x_i :$ III, 5, 1.

$(x_n)$ (series, by abuse of language) : III, 5, 6.

$\sum_{n=0}^\infty x_n, x_0 + x_1 + \cdots + x_n + \ldots, \sum_{n=0}^\infty x_n :$ III, 5, 6.

$\mathbf{P}_{n=0}^\infty x_n, \prod_{n=0}^\infty x_n :$ III, 5, 7.

$K*$ (K a division ring) : III, 6, 7.

$R, R*, R+, R*+$ : IV, 1, 3.

$\sqrt[m]{x}, \sqrt{x}, x^{1/m}$ (x real and $\geq 0$) : IV, 3, 3.

$\overline{\mathbf{R}}, + \infty, - \infty :$ IV, 4, 2.

sup A, inf A (A a subset of $\overline{\mathbf{R}}$) : IV, 4, 2.

$\overline{\mathbf{R}}^* :$ IV, 4, 3.

$\lim_{x > a, x > a, x \in A} f(x), \lim_{x > a, x < a, x \in A} f(x) :$ IV, 5, 3.

$f(a-), f(a+) :$ IV, 5, 3.

sup $f(x)$, inf $f(x)$ ($f$ a real-valued function) : IV, 5, 4.

sup $f_i$, sup $f_i$, inf $f_i$, inf $f_i$ ($f_i$ real-valued functions) : IV, 5, 5.

lim sup $\mathfrak{G} f$, lim inf $\mathfrak{G} f$, lim sup $x, \mathfrak{G} f(x)$, lim inf $x, \mathfrak{G} f(x) :$ IV, 5, 6.

lim sup $f$, lim inf $f$, lim sup $x f(x)$, lim inf $x f(x) :$ IV, 5, 6.

lim $\sup_{x > a} f(x)$, lim $\inf_{x > a} f(x) :$ IV, 5, 6.

lim $\sup_{x > a, x \in X} f(x)$, lim $\inf_{x > a, x \in X} f(x)$, lim $\sup_{x > a, x \neq a} f(x)$, lim $\inf_{x > a, x \neq a} f(x) :$ IV, 5, 6.

lim sup $u_n$, lim inf $u_n$ [($u_n$ a sequence of numbers)] : IV, 5, 6.

lim sup $f_n$, lim inf $f_n$ [($f_n$ a sequence of functions)] : IV, 5, 6.

$f + g, fg, 1/f$ ($f, g$ functions with values in $\overline{\mathbf{R}}$) : IV, 5, 7.

$[x]$ (x a real number) : IV, 8, 2.