## An Introduction to Abstract Harmonic Analysis |

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### Contents

TOPOLOGY SECTION PAGE t Sets | 1 |

Topology | 3 |

Separation axioms and theorems | 5 |

Copyright | |

31 other sections not shown

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Abelian group Baire functions Banach space Cartesian product choose closed ideal closed set closure commutative Banach algebra compact Abelian group compact Hausdorff space compact set compact subset complex numbers contains continuous complex-valued functions continuous function converges convolution Corollary coset defined dense direct sum disjoint element equivalent exists finite follows Fourier transform func function algebra G L1 given group algebra Haar measure Hausdorff space hence Hilbert space homomorphism hull idempotent includes inequality intersection inverse involution isometric isomorphic kernel left invariant Lemma linear functional locally compact Abelian locally compact group mapping maximal ideal space minimal closed multiplication neighborhood non-negative non-zero normed linear space null open set orthogonal periodic functions Plancherel theorem positive definite Proof proved real-valued regular maximal ideal representation scalar semi-simple sequence spectrum subspace summable theory tion uniform norm unique unitary weak topology zero