If I close the mail app on iPhone 5S, can I still be notified of received e-mails?

I usually try to close all apps not in use from my phone to save more battery, but I always leave the mail app running in fear that if I close it, I won't be notified when I get new e-mails. Can I close it and still be notified or not? Also, same question for Snapchat. If I close out Snapchat, can I still be notified when people send me snaps?

Settings > Notification Center > Mail > your email account(s) > Show on Lock Screen > ON?
Lock screen notification settings and if you have the email set to auto-update and push to your phone.Best luck.
http://ipod.about.com/od/iphoneemail/ss/Iphone-Email-Settings.htm

http://ipod.about.com/od/UsingiOS5/ss/Using-Notification-Center.htm

Yes you would be notified in both cases. They use Push Notifications. The app can be closed but you would be notified of activity from them.