Metric Space

Cauchy-Schwarz Inequality

Discrete Metric

an \(\epsilon\)-ball of \(x\) in \(S\)

Open Set

Metric Topology

Power Set of \( X \)

Topological Space

Closed Set

Sequence

Convergent Sequence

Convergent Subsequence

Closure of a Set

Cauchy Sequence

Bounded Set

Complete Set

Open Cover of a set \( K \)

Finite Subcover

Compact Set

Finite Intersection Property

Totally Bounded Metric Space

Connected Metric Space

Countably Infinite Set

Countable set

Dense Set

Separable

Continuity

Pointwise Convergence

Uniform Convergence

Convex Set

Convex Hull of a Set

Supremum

Infinum

\(i\)-th partial derivative

Gradient

Hessian Matrix of \( f \text{ at } x \)

Jacobian Matrix of \( f \text{ at } x \)

Differentiable Function

Taylor's Approximation

Concave Function

Convex Function

Negative semidefinite matrix

Positive semidefinite matrix

\(t\)-upper contour set

\(t\)-lower contour set

Quasiconcave Function

Quasiconvex Function

Local Maximizer/Minimizer of \(f\)

Global Maximizer/Minimizer of \(f\)

Critical Points of \(f\)

Complementary Slackness

Constraint Qualification

Correspondence

Upper Hemicontinuous Correspondence

Compact-Valued Correspondence \( \Gamma \)

Closed-Valued Correspondence \( \Gamma \)

Convex-Valued Correspondence \( \Gamma \)

Lower Hemicontinuous Correspondence

Upper Inverse Image

Lower Inverse Image

Continuous Correspondence

Closed Graph Property

Hyperplane in \( \mathbb{R}^{N} \)

Separating Hyperplane

Proper Separation of Sets

Strict Separation of Sets

Partially-Ordered Set (poset)

Partial Order

Chain

Bounds of a Poset

Supremum of \(E\) in \(X\)

Infimum of \(E\) in \(X\)

Join of \(x \text{ and } y\)

Meet of \(x \text{ and } y\)

Lattice

Sublattice

Induced Set Ordering on \( \mathcal{L} \left( X \right) \)

Complete Lattice

Subcomplete Sublattice

Increasing and Decreasing Monotone Functions

Increasing Differences

Supermodular Function

Quasisupermodular Function

Single Crossing Property