The key attribute of hyperspace is that the time it takes to travel between two points in hyperspace can be different (preferably less) than the time it takes to travel between two points in normal space (where time is measured with respect to the traveler). This makes for a handy explanation of faster than light (FTL) travel. Hyperspace is the most common device used for explaining FTL in a science fiction story where FTL is necessary for interstellar travel or intergalactic travel. Spacecraft able to use hyperspace for FTL travel are said to have hyperdrive.
Another attribute of hyperspace is that it enables time-travel. Yet because of relativity, this is not a clear idea since there is no such thing as universal time, just relative time. For example, one observer might interpret the journey as traveling into the future, another as with the present, and another as into the past, and all three may report some sort of movement in space.
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