Hilbert Space Definition Orthonormal Basis Definition Bounded Linear Operator Definition Closure of a Connected Set is Connected Topology Least-Squares Approximation via Orthogonal Polynomials Numerical Analysis Approximation of Measurable Functions by Continuous Functions Measure Theory Uniqueness Of Measure Extension Measure Theory Fundamental Solution Of Laplace's Equation Partial Differential Equations Root Test Series Mixing Estimate For Shear Flows PDE Permanence Properties of Fréchet Spaces Functional Analysis Analysis Area Functional Analysis Subarea