There are quite a few options depending on exactly what you want, so I'll list several.
Duplicate Point removal
For points that are on the same spot, there are actually a lot of transformers that will remove the duplicates as part of their process, but the one you'd want would be:
This one will only get rid of duplicate points that are on the exact same spot.
If you want to remove points that are within a certain tolerance then the
Snapper is probably the answer. Set it to "vertex snapping" and before it place a
Counter. Use the attribute that the counter creates for the "Group By" of the Snapper. This way features will only be snapped to themselves. So you'll have something like:
Input ---> Counter ---> Snapper ----> Output
The final option is to use a
generalizer (American spelling). You'll probably want to experiment to see which algorithm to use and they're designed for something slightly different.
Just using one of them (probably the snapper) should be sufficient, but you'll want to test them for best results in your situation.