Well, as at least one other commenter in this thread already pointed out, this is possible with WDS (Wireless Distribution System). However, this needs to be supported by the access points. If it is supported (for example on APs running OpenWRT), it is literally just a matter of enabling WDS on the station and client APs, and bridging the wireless interfaces to the ethernet interfaces.
I've been using this setup in my home network for years now (with a dedicated OpenWRT device for each wired "island") and it works great.
Edit: To clarify, yes, this establishes a single broadcast domain. For example, DHCP and ARP requests are propagated through the entire network.
I've been using this setup in my home network for years now (with a dedicated OpenWRT device for each wired "island") and it works great.
Edit: To clarify, yes, this establishes a single broadcast domain. For example, DHCP and ARP requests are propagated through the entire network.