Need Help with Bathroom 2 Handle Faucet

[GKB]

The hot water faucet has gotten hard to turn over the last few days. I figured it would be an easy fix, but now I can't even disassemble the thing to repair it. Attached are photos with what I am dealing with. I fully loosened the center screw that is inside the handle that I assume screws into the stem but I can't remove it or the top piece that the handle sticks out of. Nothing seems to budge. There is no set screw anywhere. I did unscrew the handle itself. It screws into the piece inside the top with the three-prong recesses. Do I need to remove the piece with the three recesses that is inside the top part? If so, is there a tool for that? Any help appreciated. Also any clues as to the faucet mfg?

 

[GKB]

Well I solved this on my own. Apparently the entire handle just screws off. The lower base is actually screwed on. So by unscrewing the central screw that screws into the valve stem and then unscrewing the lower base counterclockwise, the entire handle assembly pulls off to access the valve stem. For some reason none of the faucet repair instructions I looked at had this type of system. It was either you unscrewed the screw that screws into the stem and that's it or there is a set screw that screws in from the side.