and 
, turned out to be different functions of
Cartesian coordinates. To have a spinor space model,
you ought to use a doubling vector space
{ (x1,x2,x3 ) 
(x1,x2,x3)'}.
The main idea is to develop some mathematical
technique to work with such extended models.
Spinor fields and , given as functions of Cartesian
coordinates xi
xi', do not obey Cauchy-Riemann analyticity condition
with respect to complex variable (x1 + i x2) (x1 + i x2)'.
Spinor functions are in one-to-one correspondence with coordinates
xi xi' everywhere excluding the
whole axis (0,0,x3) (0,0,x3)'
where they have an exponential discontinuity. It is proposed to consider
properties of spinor fields (xi xi') and (xixi')
in terms of continuity with respect to geometrical directions
in the vicinity of every point.
The mapping of spinor field into and inverse
have been constructed. Two sorts of spatial spinors
are examined with the use of curvilinear coordinates (y1,y2,y3):
cylindrical parabolic, spherical and
parabolic ones. Transition from vector to spinor models is achieved by doubling
initial parameterizing domain G (y1,y2,y3) 
(y1,y2,y3) with new identification rules on the boundaries.Different spinor space models are built on explicitly different spinor
fields (y) and (y). Explicit form of the mapping spinor field (y)
of pseudo vector model into spinor (y) of properly vector one is given,
it contains explicitly complex conjugation.
Key words: space, geometry, spinor, continuity, P-orientation, spherical and parabolic coordinates
