  This article introduces proximal Cech nerves and Cech complexes, restricted
to finite, bounded regions $K$ of the Euclidean plane. A Cech nerve is a
collection of intersecting balls. A Cech complex is a collection of nerves that
cover $K$. Cech nerves are proximal, provided the nerves are close to each
other, either spatially or descriptively. A Cech nerve has an advantage over
the usual Alexandroff nerve, since we need only identify the center and fixed
radius of each ball in a Cech nerve instead of identifying the three vertices
of intersecting filled triangles (2-simplexes) in an Alexandroff nerve. As a
result, Cech nerves more easily cover $K$ and facilitate approximation of the
shapes of irregular finite, bounded planar regions. A main result of this
article is an extension of the Edelsbrunner-Harer Nerve Theorem for descriptive
and non-descriptive Cech nerves and Cech complexes, covering $K$.
