Hyperspace (science fiction), a concept often used in science fiction writing

In topology a hyperspace is a topological space whose elements are subsets of another topological space.

Minkowski spacetime, a concept, often referred to by science fiction writers as "hyperspace", that refers to the four-dimensional space-time of special relativity

Tesseract, also known as a hypercube, a cube [0,1]^d, where d > 3. The word tesseract was used, especially in nineteenth and early twentieth century British semi-popular books on mathematics, to denote the special case d = 4.

Hyperspace, a Euclidean space of dimension greater than three. (The term was common in late nineteenth century British books, sometimes in the context of paranormal fantasies, but has become rarer since then.)

Hypersphere, a round sphere dimension higher than 3, especially if embedded in such a space.

Hyperplane, an affine subspace of codimension one in such a space.

Hyperspace theory

Hyperspace (book), a book by Dr. Michio Kaku that attempts to explain the possibility of ten-dimensional space using string theory

Space (documentary), a 2001 BBC documentary that was distributed in the U.S. as Hyperspace

Hypersurface, a submanifold of codimension one, especially if embedded in such a space. This term includes hypersphere and hyperplane as special cases.