Can I Keep my email accounts after I cancel my internet?

I believe you retained them for 6 months which gives you time to switch any important financials or contacts to a public email.  

He Formerlyknowas,

Thank you for responding to my question. 

After posting my question, I spoke with two employees at local AT&T stores.  One of them seemed very sure and the other seemed very sure and very knowledgeable about Email in general and ATT Email specifically.  Both said that I would be able to keep all my @att.net emails indefinitely.  The second person said that ATT no longer manages Email servers and have farmed/sold/transferred all @att.net Email addresses to Yahoo and or others. 

He also said that should I have difficulty accessing my email addresses in the future, I could contact ATT's "ProTech" support at: att.com/myprotectadvantage or 888 477 6832, even though I was no longer a subscriber. 

Thank you again for responding to my "cry for help".  Nevertheless, I hope you are mistaken about the six-month grace period.

Kindest Regards,

Commodude

You can definitely keep your att.net email as long as you leave ATT with your account in good standing.

Thanks Sandblaster.  Your confirmation is appreciated. 

I got email at @pacbell.net in the '90s when pacific bell was my internet provider. Pacific Bell was one of the branches split off of Ma Bell for antitrust reasons. I kept that mail account at no charge long after pacbell ceased to be my provider. Then pac bell was dissolved and ATT handled the mail, but my email address was unchanged.  My username was the entire email address. Then ATT tansferred me to yahoo, still with the same email address, still no charge. There are customer service pages for email at ATT and yahoo, with links from the former to the latter. I think yahoo and AOL have always provided free email accounts, you pay by seeing adds if you log into their webmail server page.

Quick follow up question on this. When I have to login to my att.net email, its asks me to login thru my ATT account. If I cancel, how will I log in, in the future?

AT&T is no longer my ISP (verizon is). I have a mobile phone through AT&T, but it is on my wife's account, not mine. 
If I go to www.att.net, it redirects immediately to currently.att.yahoo.com. This is a news summary page, where I have option to login and check email. Login works if I use my full email address as username. There are options to remind or reset username and password (or to set up a new account). I suspect this is the same even if ATT is your ISP, in which case it is likely that nothing will change when you cancel.
If I go to www.att.com, that is a page selling AT&T phones and services. It seems I am already logged in, perhaps because I logged into the webmail server above, or perhaps because I chose "keep me logged in" last time I logged in on this computer.