At the time, the Ulysses was the closest starship in the sector and was twenty hours away, at maximum warp. However, due to sabotage to the communications system by a changeling infiltrator, the Defiant was unable to request assistance. (DS9: "The Adversary")
Background information Edit
The Ulysses was named after the Roman word for Odysseus, a hero of the Trojan War in Homer's The Iliad and the main character of Homer's The Odyssey.
The game Star Trek: Deep Space Nine - The Fallen featured a Miranda-class starship with the same name, in service in the 2360s. William Ross served on the ship as first officer. That ship was attacked by the Cardassians and crashed on an uninhabited planet, while investigating an Orb of the Pah-wraith.