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A hyperspace is a space of nonempty closed sets equipped with the Hausdor metric.
In: Lecture Series on Computer and Computational Sciences, vol. Contemporary Mathematics Hyperbolic and quasisymmetric structure of hyperspaces Leonid V. and Sánchez-Álvarez, J.M., On the Hausdorff fuzzy quasi-metric and computer sciences. and Piramuthu, S., Efficient genetic algorithm based data mining using feature selection with Hausdorff distance. and Madej, T., Structural similarity of loops in protein families: toward the understanding of protein evolution. Line-based object recognition using Hausdorff distance: from range images to molecular secondary structure. and de Vink, E.P., Denotational models for programming languages: applications of Banach's fixed point theorem. and de Vink, E.P., A metric approach to control flow semantics. and de Vink, E.P., Control Flow Semantics. and Deng, Y., A new Hausdorff distance for image matching. Sendov, B., Hausdorff distance and image processing.and Rucklidge, W.J., Comparing images using the Hausdorff distance. If you mean the hyperspace favored by SF writers, then there's no corresponding mathematical object or field. This gives a natural generalization of the classical Lower Bound Theorem for simplicial polytopes to the setting of centrally symmetric simplicial polytopes. Hyperspace is not a term commonly used in mathematics, so the simple answer is that no mathematical domain deals with hyperspaces. Stanley proved that for any centrally symmetric simplicial d-polytope P with d≥3\documentclass that satisfy this inequality as equality.