Here's a follow-up question, based on the answer given to my original question.
Suppose that my opponent controls an island, with 3 out of 5 bridges.
Suppose I build one of the other two bridges.
Now suppose my opponent builds on the fifth bridge, to have 4 out of 5.
Has he gained control of the island again, causing my bridge to be removed?
Or is my bridge safe as long as he controls that island?
The English rules which I have distinguish between "having control" and "gaining control". If you already have control, and build another bridge, it seems to me that building that bridge does not make you "gain" control. You just continue to have the control which you already had - no control was "gained".