noun Mathematics.
a Euclidean space of dimension greater than three.

1865–70; hyper- + space

hyperspatial [hahy-per-spey-shuhl] , adjective
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Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
hyperspace (ˌhaɪpəˈspeɪs)
1.  maths space having more than three dimensions: often used to describe a multi-dimensional environment
2.  (in science fiction) a theoretical dimension within which conventional space-time relationship does not apply

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

"space of more than three dimensions," 1867, from hyper- + space (n.). A hybrid; correctly formed it would be superspace.
Online Etymology Dictionary, © 2010 Douglas Harper
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Computing Dictionary

hyperspace definition

/hi:'per-spays/ A memory location that is *far* away from where the program counter should be pointing, often inaccessible because it is not even mapped in. (Compare jump off into never-never land.)
This usage is from the SF notion of a spaceship jumping "into hyperspace", that is, taking a shortcut through higher-dimensional space - in other words, bypassing this universe. The variant "east hyperspace" is recorded among CMU and Bliss hackers.
[Jargon File]

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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Example sentences
Hyperspace travel using hidden dimensions that have yet to be sensed would fall
  into this category.
In hyperspace co-dimensions the speed of light has a different value depending
  on the physics constants of the dimension.
If such center exists, it is in the higher dimension hyperspace.
With each foray into hyperspace something new is added to the craft, the orbits
  widen, the technical manuals expand.
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