Hi, All:(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to understand why covering maps have the

local triviality condition, i.e., given a cover C:X-->Y, every point y in Y

has a neighborhood Oy of y with p^-1(Oy)~ Oy x F, where F is the fiber. This

seems confusing, in that fibers of covering maps are a (discrete) collection of points

in X (since local diffeomorphisms are local bijections, the preimages are isolated/discrete)

. Does this statement just mean that the fiber is just a disjoint/discrete

collection of open sets, indexed by the cardinality of the fiber, or is there more than

that to it? I am thinking of standard examples like the covering map f:R-->$S^1$,

given by f(t)=(cost,sint), an infinite-to-one cover; would the Oy here be any 'hood

(neighborhood) of y that evenly-covers y?

Also: if this local triviality holds: is every covering map a bundle

of C over X with singletons as fibers?

Sorry, I know this is simple, but I haven't seen it in a while, and hopefully someone's

comments will jog my memory.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Local Trivialization in Covering Spaces

**Physics Forums | Science Articles, Homework Help, Discussion**