subgraph 子图
A graph H=(W,F) is a subgraph of G=(V,E) when W ⊆ V and F ⊆ E, with every edge of F having its endpoints in W.
Terminology & Translations
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subgroup 子群
A subset $H$ of a group $G$ containing the identity and closed under multiplication and inverses.
submartingale 下鞅
An integrable adapted discrete-time process $X_n$ with $E[X_{n+1}\mid\mathcal F_n]\ge X_n$ almost surely for every $n$.
submodule 子模
An additive subgroup $N$ of an $R$-module $M$ closed under the $R$-scalar action.
subsequence of a real sequence 子列
A subsequence of (a_n) is (a_{n_k}) where the positive integer indices n_k increase strictly.
subset 子集
$A$ is a subset of $B$ if $x\in A$ implies $x\in B$ for every $x$.
subspace topology 子空间拓扑
For a subset A of a topological space X, the topology on A consisting of intersections of A with open subsets of X.
sumset 和集
For subsets A,B of an additively written abelian group, their sumset A+B is {a+b:a∈A,b∈B}; each resulting element is included once, regardless of representation multiplicity.
supermartingale 上鞅
An integrable adapted discrete-time process $X_n$ with $E[X_{n+1}\mid\mathcal F_n]\le X_n$ almost surely for every $n$.
supremum of a real set 上确界
For a nonempty real set A bounded above, its supremum is the least real upper bound: it bounds every member of A and is no larger than any other upper bound.
surjective function 满射
A function f:A→B whose image is all of B.
suspension flow construction 扭扩
For a homeomorphism $T:X\to X$ of a nonempty compact metric space and a continuous roof $r:X\to(0,\infty)$, the global real-time flow on the quotient of $\{(x,s):0\le s\le r(x)\}$ identifying $(x,r(x))$ with $(Tx,0)$,…
Sylow subgroup Sylow 子群
For a finite group of order $p^am$ with prime $p$ and $p\nmid m$, a subgroup of order $p^a$.
symplectic form 辛形式
A smooth two-form on a smooth manifold whose exterior derivative is zero and whose contraction map from each tangent space to its dual is invertible.
symplectic manifold 辛流形
A smooth manifold equipped with a smooth closed two-form whose value on every tangent space is nondegenerate; closed means its exterior derivative vanishes, and nondegenerate means contraction identifies tangent and…
syntactic consistency 一致
A sentence set is syntactically consistent in a specified classical calculus if no derivation from it concludes falsity.
T1 space T1 分离公理
A topological space in which every singleton is closed.
tame ramification of p-adic local fields p 进局部域的温分歧
A finite extension $L/K$ of $p$-adic local fields is tamely ramified when $p\nmid e(L/K)$.
tangent bundle 切丛
For a smooth n-manifold, the disjoint union of all its tangent spaces, with projection sending a tangent vector to its point and smooth local trivializations obtained by differentiating coordinate charts; it is a real…
tangent space 切空间
The tangent space at an interior point of a smooth manifold, or on a manifold without boundary, is the real vector space of velocities of smooth two-sided curves through that point, identifying curves with equal…
Taylor formula with integral remainder Taylor公式
For an integer m>=0 and a real C^{m+1} function on an interval containing a and x, Taylor's formula writes f(x)=sum_{k=0}^m f^{(k)}(a)(x-a)^k/k! + (1/m!) integral_a^x (x-t)^m f^{(m+1)}(t) dt.
tempered distribution 缓增分布
A tempered distribution on R^n is a continuous linear functional on Schwartz space with its topology given by all polynomially weighted derivative seminorms.
tensor product of modules 模的张量积
For a right $R$-module $M$ and left $R$-module $N$, the abelian group representing biadditive maps satisfying $b(mr,n)=b(m,rn)$.
terminal object 终对象
An object T receiving exactly one morphism X→T from every object X of its category.
topological conjugacy 拓扑共轭
Maps $T:X\to X$ and $S:Y\to Y$ are topologically conjugate if a homeomorphism $h:X\to Y$ satisfies $h\circ T=S\circ h$.