Hide textbox and button after upload

[Paul]

I want to hide the textbox and button after a file is uploaded so that the only thing showing is the filename and remove link. This is going to be in every row of a table and the user can only upload one file per row. Is there a way to do this?

[Paul]

So I see that this can be accomplished by setting the MaxFileInputsCount to 1. When just the filename and remove link are shown after a file is uploaded, if I click the remove link the textbox and button to add a file do not reappear.