Introduction to Topology and Modern Analysis |
Contents
Sets and set inclusion | 3 |
The algebra of sets | 7 |
Functions | 14 |
Copyright | |
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arbitrary assume B*-algebra Banach algebra Banach space Banach subalgebra Boolean algebra Boolean ring called cardinal number Cauchy sequence closed linear subspace closed sets closed unit commutative compact Hausdorff space compact subspace completely regular complex numbers complex plane contains continuous mapping continuous real function convergent definition denote disjoint easy eigenvalues element equals equivalent Example exists fact function f Hilbert space homomorphism identity infinite inverse left ideal lemma linear subspace linear transformation locally compact mapping f matrix maximal ideals metric space non-empty set non-empty subset non-zero normal normed linear space one-to-one mapping open base open cover open sets open sphere operator on H orthogonal orthonormal set polynomial positive integer Problem PROOF prove reader real functions defined real line real numbers scalar multiplication self-adjoint spectral subbase suffices to show Theorem theory topological space union vector weak topology хлу