Is there a way to share a wi-fi connection over wi-fi?

Solution 1:

In order for a Mac to create a local Wi-Fi network, it needs to have a wired Internet source. So what you need to do is:

1. Connect an Ethernet cable from the router (the wired source) to a Mac.
2. On that Mac, choose System Preferences > Sharing.
3. Select Internet Sharing.
4. Choose Ethernet from the “Share your connection from” pop-up menu.
5. Select AirPort in the “To computers using” list, then click AirPort Options and give your network a name and password.
6. Connect the other computers to the new Wi-Fi network you just created.

If needed, there are more details on this Apple help page: Sharing your Internet connection.

Solution 2:

You could do it with the built-in Sharing feature (System Preferences->Sharing), but it would require two wifi cards in the device acting as the bridge. More broadly, to my knowledge, it isn't possible to share a connection in the way you are proposing with a single wifi card (though you could extend the signal, it would still be limited to the same number of connections as that is bring managed by the original access point).