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Even if one accepts that the Dominion owned the space around the wormhole - and there's nothing to support the idea that they do, other than that they say they do - it doesn't follow that they were within their rights to do what they did. Look at territorial conflicts on Earth; when Argentina invaded the Falklands, there was extensive diplomatic negotiation to try and resolve the issue. When Iraq invaded Kuwait, there was extensive diplomatic negotiation to try and resolve the issue. Hell, when Germany invaded, well, the first few places it did, the allies ignored, negotiated, and conceded again.

In each case the aggrieved power could truthfully say "you know what? We tried to resolve it, we really did, and force was our final option."

The Dominion just attacked. Had they rolled up and said "Hey, this space is ours", it's likely the Federation would have withdrawn. They didn't. Because they're assholes.

Nope you are right they are assholes. It would have been so simple for the Dominion to show up and say 'hey this is our territory' but they didn't.

Of course they were planning on invading the Alpha Quadrant anyway.