A real matrix is Hurwitz if its eigenvalues have negative real parts. The following generalisation of the Bidimensional Global Asymptotic Stability Problem (BGAS) is provided. Let
X
:
R
2
→
R
2
X:\mathbb {R}^2\to \mathbb {R}^2
be a
C
1
C^1
vector field whose Jacobian matrix
D
X
(
p
)
DX(p)
is Hurwitz for Lebesgue almost all
p
∈
R
2
p\in \mathbb {R}^2
. Then the singularity set of
X
X
is either an empty set, a one–point set or a non-discrete set. Moreover, if
X
X
has a hyperbolic singularity, then
X
X
is topologically equivalent to the radial vector field
(
x
,
y
)
↦
(
−
x
,
−
y
)
(x,y)\mapsto (-x,-y)
. This generalises BGAS to the case in which the vector field is not necessarily a local diffeomorphism.