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PDF-2De nitionsandbasicpropertiesLetGbeatopologicalgroup.AleftG-spaceisasp PDF document

U HereUGhastherightGactionughughNotethisconditionimpliesthatGactsfreelyonPandthatfactorsthroughahomeomorphism PGBthusBistheorbitspaceofPSummarizingAprincipalGbundleov

-U ? HereUGhastherightG-action(u;g)h=(u;gh).NotethisconditionimpliesthatGactsfreelyonP andthatfactorsthroughahomeomorphism :P=G!B(thusB\is"theorbitspaceofP).Summarizing:AprincipalG-bundleov

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