Hilbert space
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Hilbert spaces were a mathematical concept due to Hilbert. (PROSE: Christmas on a Rational Planet)
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A Hilbert space is a potentially infinite dimensional vector space, where given two elements of the space you can uniquely map them to a number up to complex conjugate (ie, the "projection" of one element onto another) and there are no "holes" in the space. (For example, the rational numbers would be a space with "holes" while the reals would not.)