## A general theory of fibre spaces with structure sheaf |

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### Contents

INTRODUCTION | 1 |

SHEAVES OF SETS | 16 |

GROUP BUNDLES AND SHEAVES OF GROUPS | 26 |

2 other sections not shown

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### Common terms and phrases

abelian group algebraic analytic associated fibre space Aut(E canonically isomorphic cocycle commutative composition law continuous map coordinate maps coordinate transformations corollary corresponding definition denoted equivalence relation exact sequence F into F faithful sheaf fibre bundle fibre space associated fibre space defined functor G operates germs of automorphisms germs of continuous germs of isomorphisms germs of maps group bundle group G hence interior automorphisms inverse image left operators Let F Let G Lie group locally isomorphic map f moreover natural map necessary and sufficient neutre element notion of fibre open covering open sets paracompact quotient regular representation restriction maps section of G sheaf G sheaf of germs sheaf of groups sheaf of left space of structure space with composition space with G space with structure structure group structure of type structure sheaf structure type subset subsheaf of groups system of coordinate topological group topology trivial fibre space X-homomorphism Zariski topology