If you peel and onion layer by layer, do you need to keep it in the refrigerator?

I use onions for sandwiches and I only use a little bit, so if I just used one layer of the onion, will it keep without refrigeration?
I wrap mine in plastic warp then put it in a Tupperware container that is made for an onion. its a little half round thing that can hang on the shelf in the fridge...but my shelves are glass so I just toss it in the veggie drawer and it keeps for a week or more. I have also stored chopped onion the same way for 3-4 days.



see this site for more information:

http://www.fda.gov/Food/ResourcesForYou/
You should or it will dry out. Make sure to seal it or the entire refrigerator will smell like onion.
Never, ever re-use onions, they collect bacteria like a sponge. Once you start one, finish it.
yeah,or it could spoil easily if you don