## Pacific Journal of Mathematics, Volume 8 |

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### Contents

of metric spaces | 11 |

S P Avann A numerical condition for modularity | 17 |

Raymond G Ayoub A mean value theorem for quadratic | 23 |

Copyright | |

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abelian group Amer analytic arbitrary associative algebra assume automorphism Boolean algebra boundary bounded closed coefficients commutative compact completes the proof component condition consider constant contains continuous function converges convex Corollary defined definition denote differential equations direct sum direct summand domain elements equivalent exists follows Hence hermitian homomorphism ideal idempotent identity implies inequality infinite integral interval isomorphic Jordan algebra lattice Lemma linear mapping Math matrix maximal ideal measure metric space minimal module neighborhood nilpotent non-negative non-singular norm notation obtain operator orthogonal polynomial positive number problem proof of Theorem prove real numbers regular representation respect result Riemann surface ring satisfies scalar self-adjoint semigroup sequence solution of 2.4 space spectral subalgebra subgroup submodule subset subspace Suppose topological space topology transformation uniform uniform space uniformly continuous unique vanishes vector vector space zero