  Linear topological spaces with partial ordering (linear kinematics) are
studied. They are defined by a set of 8 axioms implying that topology, linear
structure and ordering are compatible with each other. Most of the results are
valid for both the finite-dimensional and infinite-dimensional case. In
applications to physics, partial ordering is interpreted as the causal
structure. Both Newtonian and the special relativity causal structures are
studied, and some other possible types of causality are discussed.
  Linear topological spaces with pseudometric which satisfies the time
inequality instead of the triangle inequality are studied (3 axioms).
Pseudometric (which is determined by a pseudonorm) is shown to define a
topology on a linear space, it being a continuous mapping in this topology.
Proved that for a space with pseudometric to be a linear kinematics it is
necessary and sufficient that mapping of multiplication by -1 (i.e. time
reversion) be continuous. Minkovskii space of the special relativity theory
proved to be a pseudometric linear kinematics.
