Hausdorff Space Definition Topology Definition Basis Definition Dirichlet's Principle for the Neumann Problem Partial Differential Equations Kellerer Dual Attainment Theorem for Dominated Lower Semicontinuous Costs Analysis First-Order Taylor Approximation Analysis Equivalence Between a Higher-Order Scalar ODE and Its Companion First-Order System Analysis Second-Order Heisenberg Normal Form for Strictly Pseudoconvex Hypersurfaces Analysis Holomorphicity of Power Series Complex Analysis Ball Polyconvex Sequential Weak Lower Semicontinuity Theorem Analysis Saddle-Node Bifurcation Dynamical Systems Analysis Area