General Does android your own email account?

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http://androidforums.com – I have my own domain name and webhosting, and I use IMAP email with that. I think Android doesn't allow you to do that kind of email. It only allows four types of email accounts: gmail, hotmail, Yahoo!, and AOL. Is that true? I couldn't use my own email last time I had Android, which was when I had a Verizon Motorola Droid II in 2011. I had to use gmail...ugh. This is why I prefer my Palm Treo 7.0 p. That lets you use any email out there. Do you know will the Samsung Galaxy Note II support my own IMAP email? Or will Blackberry Q10? I prefer a physical qwerty keyboard and a giant touchscreen (General)