Errata fixed in section 19 (Principal Bundles)#4
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Satisfying (i), require p<|e=p instead of p<|g=p.
Require q=g|>p for some g rather than p=g|>p.
p element of base manifold M rather than of group G.
L_pM isomorphic as a Lie Group, not as vector space, to GL(d,R).
T_pM -> L_pM
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Several minor typographical/mathematical errors corrected.