There is one Information Retrieval model that uses geometrical space: it is the Vector Space Model, which is defined in Euclidean Space. The paper shows that it is possible to define a Vector Space Model in non-Euclidean Space, too. Namely, the paper proposes a Vector Space Model over the Cayley-Klein Hyperbolic Geometry using a similarity measure derived from the hyperbolic distance. It is sho...

in this paper, after reviewing some results in minimal space, some new results in this setting are given. we prove a generalized form of the fan-kkm typetheorem in minimal vector spaces. as some applications, the open type of matching theorem and generalized form of the classical kkm theorem in minimal vector spaces are given.