  Usually a Riemannian geometry is considered to be the most general geometry,
which could be used as a space-time geometry. In fact, any Riemannian geometry
is a result of some deformation of the Euclidean geometry. Class of these
Riemannian deformations is restricted by a series of unfounded constraints.
Eliminating these constraints, one obtains a more wide class of possible
space-time geometries (T-geometries). Any T-geometry is described by the world
function completely. T-geometry is a powerful tool for the microcosm
investigations due to three its characteristic features: (1) Any geometric
object is defined in all T-geometries at once, because its definition does not
depend on the form of world function. (2) Language of T-geometry does not use
external means of description such as coordinates and curves; it uses only
primordially geometrical concepts: subspaces and world function. (3) There is
no necessity to construct the complete axiomatics of T-geometry, because it
uses deformed Euclidean axiomatics, and one can investigate only interesting
geometric relations. Capacities of T-geometries for the microcosm description
are discussed in the paper. When the world function is symmetric and T-geometry
is nondegenerate, the particle mass is geometrized, and nonrelativistic quantum
effects are described as geometric ones, i.e. without a reference to principles
of quantum theory. When world function is asymmetric, the future is not
geometrically equivalent to the past, and capacities of T-geometry increase
multiply. Antisymmetric component of the world function generates some metric
fields, whose influence on geometry properties is especially strong in the
microcosm.
