1. CMB 2013 (vol 57 pp. 364)
 Li, Lei; Wang, YaShu

How Lipschitz Functions Characterize the Underlying Metric Spaces
Let $X, Y$ be metric spaces and $E, F$ be Banach spaces. Suppose that
both $X,Y$ are realcompact, or both $E,F$ are realcompact.
The zero set of a vectorvalued function $f$ is denoted by $z(f)$.
A linear bijection $T$ between local or generalized Lipschitz vectorvalued function spaces
is said to preserve zeroset containments or nonvanishing functions
if
\[z(f)\subseteq z(g)\quad\Longleftrightarrow\quad z(Tf)\subseteq z(Tg),\]
or
\[z(f) = \emptyset\quad \Longleftrightarrow\quad z(Tf)=\emptyset,\]
respectively.
Every zeroset containment preserver, and every nonvanishing function preserver when
$\dim E =\dim F\lt +\infty$, is a weighted composition operator
$(Tf)(y)=J_y(f(\tau(y)))$.
We show that the map $\tau\colon Y\to X$ is a locally (little) Lipschitz homeomorphism.
Keywords:(generalized, locally, little) Lipschitz functions, zeroset containment preservers, biseparating maps Categories:46E40, 54D60, 46E15 

2. CMB 2010 (vol 53 pp. 466)
 Dubarbie, Luis

Separating Maps between Spaces of VectorValued Absolutely Continuous Functions
In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vectorvalued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and biseparating in the finitedimensional case. The infinitedimensional case is also studied.
Keywords:separating maps, disjointness preserving, vectorvalued absolutely continuous functions, automatic continuity Categories:47B38, 46E15, 46E40, 46H40, 47B33 
