  In this article we examine T-dualization in double space formalism of type II
superstring theory in pure spinor formulation. Background fields that we
consider will all be constant except Ramond-Ramond field which will
infinitesimally depend only on bosonic coordinates $x^\mu$. In double space
T-dual transformations are represented as permutations between starting $x^\mu$
and dual coordinates $y_\mu$. Combining these two sets of coordinates into
double coordinate $Z^M = (x^\mu, y_\mu)$ while demanding that T-dual double
coordinates have same transformation laws, we obtain how background fields
transform under T-duality. Comparing these results with ones obtained with
Buscher T-dualization procedure we are able to conclude that these two
approaches are equivalent for cases where background fields have coordinate
dependence.
