Banach Space Definition Bounded Linear Operator Definition Compact Operator Definition Parabolic Harnack Inequality PDE Fourier Transform as Automorphism of Schwartz Space Harmonic Analysis Lebesgue Density Theorem Measure Theory Existence of Square Root of Two Real Numbers Fefferman–Stein Sharp Maximal Inequality Analysis Compact Subspaces and Hausdorff Spaces Topology Adjoint Operator Norm Inequality Functional Analysis Ternary Characterisation of the Cantor Set Real Analysis Analysis Area