Question : Problem: How to tell which device wireless adapter connected to: Access Point or Router

I have wireless and wired network.  I have a Linksys wireless/wired Router (WRT54G) on the 1st floor of my office building, then on the second floor of the building I have a Linksys Wireless Access Point (WAP54G) setup as an Access Point with it connected to my wired network through a patch panel (router connected to same patch panel).  This access point is in an office on the 2nd floor.  In this same office is a notebook with a wireless adapter.  Before I put in the access point I could barely pickup the wireless router on the 1st floor (low signal), kept dropping connection, but sometimes I did get a good signal from the router.  So I added the access point.  I assume that this 2nd fl. notebook wireless adapter is connecting to the 2nd fl. access point since there are only about 6 ft. apart, but how do I know for sure?  The real question:
1.) When you have 2 devices, access point and router, where either one could make the radio connection to a notebook wireless adaptere, how do you know which one the wireless adapter is actually connected to?
Thanks,
Joe

Answer : Problem: How to tell which device wireless adapter connected to: Access Point or Router

Assuming both the devices use the same SSID, the client (notebook) would choose the strongest signal and when you move from one floor to the other, should start communicating with the other AP closest to it seemlessly. However, all this per the standards. Your experience depends on the wireless drivers you have.