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Created by Eric Andersen
almost 9 years ago
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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