One of the few root TLDs that sport a website is .ai, with OIS at ai. (http://ai./), a valid URL, yet refused by many validators (such as HN submit).
Not to be confused with www.* domains like com (http://www.com).
Some browsers may redirect ai (a local hostname) to ai.. Bevahior varies. Another glitch: ftp.TLD domains are valid and used, yet when entered into most browsers, they will change the protocol to ftp before even trying to access ftp.TLD over HTTP.