  By constructing a nilpotent extended BRST operator $\bs$ that involves the
N=2 global supersymmetry transformations of one chirality, we show that the
standard N=2 off-shell Super Yang Mills Action can be represented as an exact
BRST term $\bs \Psi$, if the gauge fermion $\Psi$ is allowed to depend on the
inverse powers of supersymmetry ghosts. By using this nonanalytical structure
of the gauge fermion (via inverse powers of supersymmetry ghosts), we give
field redefinitions in terms of composite fields of supersymmetry ghosts and
N=2 fields and we show that Witten's topological Yang Mills theory can be
obtained from the ordinary Euclidean N=2 Super Yang Mills theory directly by
using such field redefinitions. In other words, TYM theory is obtained as a
change of variables (without twisting). As a consequence it is found that
physical and topological interpretations of N=2 SYM are intertwined together
due to the requirement of analyticity of global SUSY ghosts. Moreover, when
after an instanton inspired truncation of the model is used, we show that the
given field redefinitions yield the Baulieu-Singer formulation of Topological
Yang Mills.
