Bourbaki

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指标的记号

参考号数表示章、截面和小节,其中序。 (R 指结果摘要。)

□\square、τ\tau、∨\vee、¬\neg、⇒\Rightarrow:I.1.1

τx(A)\tau_x(A)、(B∣x)A(B\mid x)A、A{x}A\{x\}、A{x,y}A\{x,y\}、A{B}A\{B\}、A{B,C}A\{B,C\}:I.1.1

不是 (A)(A)、(A)(A) 或 (B)(B)、(A)⇒(B)(A)\Rightarrow(B):I.2

“AA 和 BB”:I.3.4

⟺\Longleftrightarrow, A⟺BA\Longleftrightarrow B : I.3.5

(∃x)R(\exists x)R, (∀x)R(\forall x)R : I.4.1

(∃Ax)R(\exists_Ax)R, (∀Ax)R(\forall_Ax)R : I.4.4

==、≠\ne、T=UT=U、T≠UT\ne U:I.5.1

∈\in、∉\notin、T∈UT\in U、T∉UT\notin U:II.1.1

⊂\subset、⊃\supset、⊄\not\subset、⊅\not\supset、x⊂yx\subset y、x⊃yx\supset y:II.1.2

CollxR\mathrm{Coll}_xR, εx(R)\varepsilon_x(R) : II.1.4

{x,y}\{x,y\}, {x}\{x\} : II.1.5

CXAC_XA、X−AX-A、CACA、∅\varnothing : II.1.7

⊃\supset、(T,U)(T,U)、pr⁡1z\operatorname{pr}_1z、pr⁡2z\operatorname{pr}_2z:II.2.1

A×BA\times B、A×B×CA\times B\times C、A×B×C×DA\times B\times C\times D、(x,y,z)(x,y,z):II.2.2

pr⁡1⟨G⟩\operatorname{pr}_1\langle G\rangle、pr⁡2⟨G⟩\operatorname{pr}_2\langle G\rangle、pr⁡1G\operatorname{pr}_1G、pr⁡2G\operatorname{pr}_2G(图):II.3.1

G⟨X⟩G\langle X\rangle、G(X)G(X)、G(x)G(x)(G 图形、X 集合、x 对象):II.3.1

Γ⟨X⟩\Gamma\langle X\rangle、Γ(X)\Gamma(X)、Γ(x)\Gamma(x)(Γ\Gamma对应、X集合、x 一个对象):II.3.1

G−1\overset{-1}{G}(G图),Γ−1\overset{-1}{\Gamma}(Γ\Gamma对应):II.3.2

G′∘GG'\circ G、G′GG'G(G、G' 图)、Γ′∘Γ\Gamma'\circ\Gamma、Γ′Γ\Gamma'\Gamma(Γ\Gamma、Γ′\Gamma' 对应):II.3.3

ΔA\Delta_A、IAI_A(A 集合):II.3.3

f(x)f(x)、fxf_x (f 函数)、F(x)F(x)、FxF_x(F 函数图):II.3.4

f:A→B, A→fB:II.3.4f : \mathrm{A} \to \mathrm{B},\ A \xrightarrow{f} \mathrm{B} : \mathrm{II}.3.4 x→T (x∈A, T∈C), x→T (x∈A), x→T, (T)x∈A, T (by abuse of language) (T a term):II.3.6x \to T\ (x \in A,\ T \in C),\ x \to T\ (x \in A),\ x \to T,\ (T)_{x\in A},\ T\ (\text{by abuse of language})\ (T\text{ a term}) : \mathrm{II}.3.6 pr⁡1, pr⁡2:II.3.6\operatorname{pr}_1,\ \operatorname{pr}_2 : \mathrm{II}.3.6 gf (g,f mappings) (by abuse of language):II.3.7gf\ (g,f\text{ mappings})\ (\text{by abuse of language}) : \mathrm{II}.3.7 f(x,y), f(⋅,y), f(x,⋅), f( ,y), f(x, ):II.3.9f(x,y),\ f(\cdot,y),\ f(x,\cdot),\ f(\ ,y),\ f(x,\ ) : \mathrm{II}.3.9 u×v (u,v functions), (u,v) (by abuse of language):II.3.9u\times v\ (u,v\text{ functions}),\ (u,v)\ (\text{by abuse of language}) : \mathrm{II}.3.9
⋃i∈IXi, ⋂i∈IXi:II.4.1\bigcup_{i\in I}X_i,\ \bigcap_{i\in I}X_i : \mathrm{II}.4.1
⋃X∈EX, ⋂X∈EX:II.4.1\bigcup_{X\in\mathfrak{E}}X,\ \bigcap_{X\in\mathfrak{E}}X : \mathrm{II}.4.1
A∪B, A∪B∪C, A∩B, A∩B∩C:II.4.5A\cup B,\ A\cup B\cup C,\ A\cap B,\ A\cap B\cap C : \mathrm{II}.4.5 {x,y,z}:II.4.5\{x,y,z\} : \mathrm{II}.4.5 P(X):II.5.1\mathfrak{P}(X) : \mathrm{II}.5.1 F(E,F), FE:II.5.2\mathfrak{F}(E,F),\ F^E : \mathrm{II}.5.2
∏i∈IXi, pr⁡i:II.5.3\prod_{i\in I}X_i,\ \operatorname{pr}_i : \mathrm{II}.5.3
pr⁡J:II.5.4\operatorname{pr}_J : \mathrm{II}.5.4 (gi)i∈I (extension to products of the family (gi)i∈I, by abuse of language):II.5.7(g_i)_{i\in I}\ (\text{extension to products of the family }(g_i)_{i\in I},\ \text{by abuse of language}) : \mathrm{II}.5.7 x≡y(modR) (R an equivalence relation):II.6.1x\equiv y\pmod R\ (R\text{ an equivalence relation}) : \mathrm{II}.6.1 E/R (E a set, R an equivalence relation):II.6.2E/R\ (E\text{ a set},\ R\text{ an equivalence relation}) : \mathrm{II}.6.2 RA (R an equivalence relation, A a set):II.6.6R_A\ (R\text{ an equivalence relation},\ A\text{ a set}) : \mathrm{II}.6.6 R/S (R,S equivalence relations):II.6.7R/S\ (R,S\text{ equivalence relations}) : \mathrm{II}.6.7 R×R′ (R,R′ equivalence relations):II.6.8R\times R'\ (R,R'\text{ equivalence relations}) : \mathrm{II}.6.8 x≤y, y≥x, x≰y:III.1.3x\leq y,\ y\geq x,\ x\nleq y : \mathrm{III}.1.3 x<y, y<x:III.1.3x<y,\ y<x : \mathrm{III}.1.3 sup⁡EX, inf⁡EX:III.1.9\sup_E X,\ \inf_E X : \mathrm{III}.1.9 sup⁡X, inf⁡X:III.1.9\sup X,\ \inf X : \mathrm{III}.1.9 sup⁡(x,y), inf⁡(x,y):III.1.9\sup(x,y),\ \inf(x,y) : \mathrm{III}.1.9
sup⁡x∈Af(x), inf⁡x∈Af(x):III.1.9\sup_{x\in A}f(x),\ \inf_{x\in A}f(x) : \mathrm{III}.1.9
sup⁡x∈Ax, inf⁡x∈Ax:III.1.9\sup_{x\in A}x,\ \inf_{x\in A}x : \mathrm{III}.1.9
[a,b], [a,b[, ]a,b], ]a,b[:III.1.13[a,b],\ [a,b[,\ ]a,b],\ ]a,b[ : \mathrm{III}.1.13 [←,a], ]←,a[, ]a,→[, [a,→[:III.1.13[\leftarrow,a],\ ]\leftarrow,a[,\ ]a,\rightarrow[,\ [a,\rightarrow[ : \mathrm{III}.1.13
∑i∈IEi, (ordinal sum):III.1, Exercise 3\sum_{i\in I}E_i,\ (\text{ordinal sum}) : \mathrm{III}.1,\ \text{Exercise 3}
Sx:III.2.1S_x : \mathrm{III}.2.1

Is⁡(Γ,Γ′), Ord⁡(E), λ<μ, ∑i∈Iλi, ∏i∈Iλi, λ+μ, μλ, λ∗(λ,μ,λ,order-types)\operatorname{Is}(\Gamma,\Gamma'),\ \operatorname{Ord}(E),\ \lambda<\mu,\ \sum_{i\in I}\lambda_i,\ \prod_{i\in I}\lambda_i,\ \lambda+\mu,\ \mu\lambda,\ \lambda^*(\lambda,\mu,\lambda,\text{order-types}) : III.2, 习题 13

ξη\xi^\eta(ξ,η\xi,\eta序数词):III.2、习题 18

Eq⁡(X,Y), Card⁡(X)\operatorname{Eq}(X,Y),\ \operatorname{Card}(X) : III.3.1

0,1,20,1,2 : III.3.1

c≤d\mathfrak{c}\leq\mathfrak{d}(c,d\mathfrak{c},\mathfrak{d}基数):III.3.2

sup⁡i∈Iai, ((ai)i∈I\sup_{i\in I}a_i,\ ((a_i)_{i\in I}红衣主教家族):III.3.2

∑i∈Iai, ∏i∈Iai, ∏i∈I((ai)i∈I\sum_{i\in I}a_i,\ \prod_{i\in I}a_i,\ \prod_{i\in I}((a_i)_{i\in I}红衣主教家族):III.3.3

a+b, aba+b,\ ab(a,ba,b基数):III.3.3

aba^b(a,ba,b红衣主教):III.3.5

3,43,4 : III.4.1

a−ba-b (a,ba,b 整数, b<ab<a) : III.5.2

(ti)i∈I, (ti)a≤i≤b(t_i)_{i\in I},\ (t_i)_{a\leq i\leq b} : III.5.4

∏i∈IXi, ∏i=abXi\prod_{i\in I}X_i,\ \prod_{i=a}^{b}X_i : III.5.4

φA\varphi_A (AA 子集 / 集合 EE) : III.5.5

ab, a/b\frac{a}{b},\ a/b (a,ba,b 整数 bb 除 aa) : III.5.6

5,6,7,8,95,6,7,8,9 : III.5.7

n!n! (nn 整数) : III.5.8

(np)\binom{n}{p} (n,pn,p 整数) : III.5.8

N, ℵ0\mathbf{N},\ \aleph_0 : III.6.1

(xn)n∈N, (xn)k≤n, (xn)n≥k, (xn)(x_n)_{n\in\mathbf{N}},\ (x_n)_{k\leq n},\ (x_n)_{n\geq k},\ (x_n) : III.6.1

∏n∈NXn, ∏n=k∞Xn\prod_{n\in\mathbf{N}}X_n,\ \prod_{n=k}^{\infty}X_n : III.6.1

fnf^n (ff 映射) : III.6.2

ωα, ℵα\omega_\alpha,\ \aleph_\alpha(α\alpha序数):III.6、习题 10

lim⁡←Eα\lim_{\leftarrow}E_\alpha (EαE_\alpha 集合) : III.7.1

lim⁡←uα\lim_{\leftarrow}u_\alpha (uαu_\alpha 映射) : III.7.2

lim⁡α,λ←Eαλ, lim⁡α←Eαλ, lim⁡α,λ←uαλ, lim⁡α←uαλ\lim_{\alpha,\lambda\leftarrow}E^\lambda_\alpha,\ \lim_{\alpha\leftarrow}E^\lambda_\alpha,\ \lim_{\alpha,\lambda\leftarrow}u^\lambda_\alpha,\ \lim_{\alpha\leftarrow}u^\lambda_\alpha : III.7.3

lim⁡α←Eα\lim_{\alpha\leftarrow}E_\alpha (EαE_\alpha 集合) : III.7.5

lim⁡α→uα\lim_{\alpha\rightarrow}u_\alpha (uαu_\alpha 映射) : III.7.6

lim⁡α,λ→Eαλ, lim⁡α→Eαλ, lim⁡α,λ→uαλ, lim⁡α→uαλ:\displaystyle \lim_{\overrightarrow{\alpha,\lambda}} E_\alpha^\lambda,\ \lim_{\overrightarrow{\alpha}} E_\alpha^\lambda,\ \lim_{\overrightarrow{\alpha,\lambda}} u_\alpha^\lambda,\ \lim_{\overrightarrow{\alpha}} u_\alpha^\lambda :III.7.7

S(E1,…,En)S(E_1,\ldots,E_n)(三梯队构造概形、E1,…,EnE_1,\ldots,E_n集合): IV.1.1

⟨f1,…,fn⟩s\langle f_1,\ldots,f_n\rangle^s(三梯队构造概形、f1,…,fnf_1,\ldots,f_n映射): IV.1.1

R{x,y,z}R\{x,y,z\}:R.1.2

=,≠=,\ne:R.1.6

∈,∉\in,\notin:R.1.7

∁A, E−A\complement A,\ E-A:R.1.7

∅\varnothing:R.1.8

{a}\{a\}:R.1.9

P(E)\mathfrak{P}(E):R.1.10

⊂,⊃,⫋,⫌\subset,\supset,\subsetneqq,\supsetneqq:R.1.12

∪,∩\cup,\cap:R.1.13

{x,y,z}\{x,y,z\}:R.1.13

XAX_A(X子集):R.1.16

EA\mathscr{E}_A(E\mathscr{E}集合/子集):R.1.16

f(x), fx, x→f(x)f(x),\ f_x,\ x\to f(x)(ff映射、xx元素):R.2.2

f(X)f(X)(X子集):R.2.4

f−1f^{-1}(ff映射):R.2.6

g∘f, h∘g∘fg\circ f,\ h\circ g\circ f(f,g,hf,g,h映射):R.2.11

fAf_A(ff映射):R.2.13

(xi)i∈I, (xi)(x_i)_{i\in I},\ (x_i):R.2.14

(x,y)(x,y):R.3.1

E×FE\times F(E、F集合):R.3.1

pr⁡1,pr⁡2\operatorname{pr}_1,\operatorname{pr}_2:R.3.1

Δ\Delta:R.3.4

Z−1Z^{-1}(乘积的Z子集):R.3.4

K(X)K(X)(E×FE\times F的K子集,E的X子集):R.3.6

K(x)K(x)(E×FE\times F的K子集,E的x元素):R.3.9

B∘A, BA, C∘B∘A, CBAB\circ A,\ BA,\ C\circ B\circ A,\ CBA(E×FE\times FA子集、F×GF\times GB子集、G×HG\times HC子集):R.3.10

(x,y,z)(x,y,z):R.3.12

E×F×GE\times F\times G:R.3.12

pr⁡1,2\operatorname{pr}_{1,2}:R.3.12

(f,g,h) (f,g,h mappings):R.3.12(f,g,h)\ (f,g,h\ mappings) : R.3.12
⋃i∈IXi,⋃iXi,⋃X∈FX:R.4.4 \bigcup_{i\in I} X_i,\quad \bigcup_i X_i,\quad \bigcup_{X\in\mathfrak{F}} X : R.4.4
⋂i∈IXi,⋂iXi,⋂X∈FX:R.4.9 \bigcap_{i\in I} X_i,\quad \bigcap_i X_i,\quad \bigcap_{X\in\mathfrak{F}} X : R.4.9
∏i∈IXi,∏iXi:R.4.9 \prod_{i\in I} X_i,\quad \prod_i X_i : R.4.9
EI (E,I sets):R.4.9E^I\ (E,I\ sets) : R.4.9 pr⁡J,pr⁡X:R.4.11\operatorname{pr}_J,\operatorname{pr}_X : R.4.11 (fI) (fI mappings):R.4.13(f_I)\ (f_I\ mappings) : R.4.13 E/R (E a set, R an equivalence relation on E):R.5.2E/R\ (E\ a\ set,\ R\ an\ equivalence\ relation\ on\ E) : R.5.2 RA (R an equivalence relation, A a subset):R.5.5R_A\ (R\ an\ equivalence\ relation,\ A\ a\ subset) : R.5.5 T/R (T, R equivalence relations):R.5.9T/R\ (T,\ R\ equivalence\ relations) : R.5.9 R×S (R, S equivalence relations):R.5.10R\times S\ (R,\ S\ equivalence\ relations) : R.5.10 N:R.6.2N : R.6.2 ≤, ≥, <, >:R.6.3\leq,\ \geq,\ <,\ > : R.6.3 [a,b],[a,b[,]a,b],]a,b[,]←,a],]←,a[,[a,→[,]a,→[,]←,→[:R.6.4[a,b],\quad [a,b[,\quad ]a,b],\quad ]a,b[,\quad ]\leftarrow,a],\quad ]\leftarrow,a[,\quad [a,\to[,\quad ]a,\to[,\quad ]\leftarrow,\to[ : R.6.4 sup⁡EX, sup⁡X, inf⁡EX, inf⁡X:R.6.7\sup_E X,\ \sup X,\ \inf_E X,\ \inf X : R.6.7
sup⁡x∈Af(x),inf⁡x∈Af(x):R.6.7 \sup_{x\in A} f(x),\quad \inf_{x\in A} f(x) : R.6.7
lim⁡⟶(Eαβ,fβα),lim⁡⟶Eα,lim⁡⟶uα:R.6.13 \underset{\longrightarrow}{\lim}(E_{\alpha\beta},f_{\beta\alpha}),\quad \underset{\longrightarrow}{\lim}E_\alpha,\quad \underset{\longrightarrow}{\lim}u_\alpha : R.6.13
lim⁡⟵(Eαβ,fαβ),lim⁡⟵Eα,lim⁡⟵uα:R.6.14 \underset{\longleftarrow}{\lim}(E_{\alpha\beta},f_{\alpha\beta}),\quad \underset{\longleftarrow}{\lim}E_\alpha,\quad \underset{\longleftarrow}{\lim}u_\alpha : R.6.14
(xn),(xm,n) (m,n natural integers):R.7.8(x_n),\quad (x_{m,n})\ (m,n\ natural\ integers) : R.7.8
Google 翻译生成的粗略草稿,质量较低。术语依照术语表,但句子可能有误;之后会由仔细的译文取代。