Can time capsule extend a wireless network using a wireless connection to it rather than being connected to Ethernet?

Apple routers cannot be used as repeater (extend wireless in apple speak) unless it connects to another apple router.. it is 100% proprietary setup.

Most colleges will have rules that you cannot use routers or wireless extenders anyway.. try and imagine what a 100 room college looks like when every student runs their own wireless AP.. chaos inc.

The best way to do backups is with a USB portable drive plugged directly into the Mac.

I think that you're saying that the airport time capsule cannot be wirelessly connected to another non-Apple wireless router (via Ethernet).

I do not understand the bit in brackets..

The first part of the statement is 90% correct.. and as far as Apple is concerned is now 100% correct as they removed the options to join a wireless network. Whatever it is 100% not going to work in a dorm room without ethernet.. so that is for sure.

This is a little surprising since they both use standard 802.11a/n,

Wireless repeater .. which is what you want is not part of the IEEE standard since the days of WEP security. The fact that both devices use 802.11a/n is irrelevant.. they cannot join to each other by wireless. Unless you use WEP security.. because when WPA with rotating keys came in .. no method was devised to work out WDS with that system. Each manufacturer used their own system.

It is possible to use use a double link..

ie you need a wireless bridge.. that will pick up a wifi signal and give you ethernet connection. An airport express can do this. And no other apple router.

But any wireless bridge will do the same thing at half the price of an express. Still for Apple stuff an express is a neat combo.

Once you have ethernet.. you can then plug the Apple Router into that and run it as a secondary router.. You will then have double NAT (maybe triple NAT) issues.

College systems are designed to prevent people doing this. They will track down and do their best to stop people using wireless or any system that can interfere with wifi access for everyone.. you are not allowed to plug a router into their systems.. whether by wireless or ethernet. If you manage to bypass that.. which will depend on the policy of the place.. it is still an extremely messy setup. And will actually cause websites not to load and other issues long term.

Bob Timmons has given the method in his classic hotel room use wifi setup.

Will the airport express help with wifi in hotel rooms?

This is fine for travelling.. not so great for everyday.

I think that you're saying that the airport time capsule cannot be wirelessly connected to another non-Apple wireless router (via Ethernet).

No, LaPastenague is saying that an AirPort Time Capsule cannot wirelessly extend the signal provided by a 3rd party router. In other words, the connection between the 3rd party router and the Time Capsule cannot be wireless only.

The AirPort Time Capsule can extend the network from any router if it is connected back to the router using a permanent wired Ethernet cable connection......and.....the Time Capsule is set up to create a wireless network that uses the same wireless network name, same wireless security setting and same password as the "main" wireless network.