Ask HN: How can a domain not have a TLD?

They don't resolve for me and most people on the public internet, but your DNS service may be configured differently. In corporate environments, bare names (like http://wiki) are often used, so DNS supports it. If you use a cheap ISP, they may try to monetize typos by making bare words resolve to a page of ads.

http://user works for me on Firefox, directing me to user.com. However, when I look at the DNS requests, my DNS server says there is no such name as "user". Right after that, a request is made for "www.user.com" then "user.com". I think Firefox is simply guessing the TLD in this case when just trying the name as provided fails and it's a TLD with no SLD (second-level domain).

That said, http://ai does work at the DNS level. It's not that the domain has no TLD, but rather that the name is just the TLD.

Take a look at https://tools.ietf.org/html/rfc3397 for one way to get this set up. Your DHCP server can give you a list of host suffixes to try whenever you have a short name.