Quitting eBay application Is there any way to quit the eBay app, so that I stop receiving all these event notifications? I like notifications, but only when I decide to run the eBay application...
Since Jelly Bean (Android 4.1), it's possible to disable notifications for individual apps. Long-press on the notification and go to App Info or go to Settings -&gt; Apps and then choose the eBay app. Uncheck the Show Notifications checkbox (detailed description with video here).

Notifications are most useful if an app needs your attention but is currently not in your focus. So i don't think there is a system setting that allows to stop notifications when the app is closed and to reactivate them if the app is started. 

Maybe you can send a feature request if that setting would make sense for this individual app. You can contact their mobile support team, find out how on google play.