Compact Linear Operator 紧算子
A compact linear operator sends bounded sets to sets with compact closure, allowing subsequence arguments in infinite-dimensional problems.
Mathematics Encyclopedia
150 original explanations and 60 external reading guides. Choose a learning direction · Contribute
No matching entries. Clear filters or try another keyword.
Compactness of First-Order Logic 一阶逻辑紧致性定理
A set of first-order sentences has a model exactly when each of its finite subsets has a model.
Completeness of First-Order Logic 一阶逻辑完全性定理
Classical first-order semantic consequence coincides with formal derivability in a sound complete calculus.
Conditional Expectation 条件期望
Conditional expectation averages an integrable random variable while preserving exactly the information in a specified sigma-algebra.
Conditional Probability 条件概率
Conditioning on a positive-probability event restricts and renormalizes a probability law.
Connected Space 连通
Connectedness expresses that a space cannot be separated into two disjoint open pieces.
Continuous Function 连续函数
Continuity expresses local control of output error by sufficiently small input error.
Continuum Hypothesis 连续统假设
The continuum hypothesis states that the cardinality of the real numbers is the least uncountable cardinal.
Convergence in Distribution 依分布收敛
Convergence in distribution compares probability laws through continuity points of their distribution functions, without requiring samplewise closeness.
Cotangent Complex
The cotangent complex extends the module of differentials by retaining homological information from a resolution. Start with a ring map and its polynomial resolution, then read how the construction localizes on affine charts of a scheme morphism.
Countable Set 可数集
A countable set is finite or can be listed by the natural numbers without omission or repetition.
Covering Space 覆盖空间
A covering space is a space lying over another in locally separate sheets.
Crystalline Cohomology
Crystalline cohomology uses divided-power thickenings to study geometry in characteristic p. Begin by identifying the objects of the crystalline site, then follow the affine reduction that turns its cohomology into an algebraic problem.
cup product 杯积
The cup product adds multiplication to cohomology groups. Compare its cochain definition with the surface calculation to see what information survives beyond the ranks of the groups.
Curvature of a Riemannian Metric 曲率张量
The Riemann curvature tensor measures the failure of covariant derivatives for the Levi–Civita connection to commute after correcting for the Lie bracket.
CW complex CW-复形
A CW complex is assembled by attaching disks along their boundary spheres, dimension by dimension. Spheres and projective spaces illustrate how the attaching maps carry information beyond cell counts.
de Rham Cohomology de Rham 上同调
de Rham cohomology measures the failure of closed differential forms to have global primitives.
Dedekind Zeta Function 戴德金 ζ 函数
The Dedekind zeta function counts integral ideals by norm, with an Euler product encoding prime splitting and a residue encoding the class number and units.
Deligne–Mumford Stack
A Deligne–Mumford stack admits a surjective étale atlas by a scheme. Compare its atlas condition with the smooth atlas used for general algebraic stacks, using the discussion of stable curves to orient further reading.
Derivative of a Real Function 导数
The derivative is the coefficient of a first-order local linear approximation to a real function.
Derived Scheme
A derived scheme equips a space with a structure sheaf of simplicial commutative rings, retaining higher homotopy information beyond an ordinary scheme. Begin with the scheme truncation and quasi-coherence conditions in Definition 2.5, then read the following adjunction to see how ordinary schemes embed and truncation recovers the underlying classical scheme.
Devaney Chaos and Other Chaos Notions Devaney混沌
Devaney chaos combines topological transitivity and dense periodic points under an explicit metric-space convention, and differs from other chaos criteria.
Diagonalizable Linear Map 可对角化线性映射
An endomorphism of a finite-dimensional vector space is diagonalizable when the space has a basis of eigenvectors.
Differential Form 外微分形式
Differential forms are the natural objects integrated over oriented curves, surfaces, and higher-dimensional manifolds.
Differential Graded Category dg-范畴
A differential graded category retains complexes of morphisms and composition compatible with their differentials.