Linear spaces of kinematic type

Linear topological spaces with partial ordering are studied. It is assumed that the above-mentioned three structures are related to each other by a set of 8 axioms. Most of the results are valid for both the finite-dimensional and the infinite-dimensional case. In applications to physics, partial ordering is interpreted as the causal structure. Both the Newtonian and the special relativity causal structure are studied, and some other possible types of causality are discussed.