  The solar magnetic field is the primary agent that drives solar activity and
couples the Sun to the Heliosphere. Although the details of this coupling
depend on the quantitative properties of the field, many important aspects of
the corona - solar wind connection can be understood by considering only the
general topological properties of those regions on the Sun where the field
extends from the photosphere out to interplanetary space, the so-called open
field regions that are usually observed as coronal holes. From the simple
assumptions that underlie the standard quasi-steady corona-wind theoretical
models, and that are likely to hold for the Sun, as well, we derive two
conjectures on the possible structure and dynamics of coronal holes: (1)
Coronal holes are unique in that every unipolar region on the photosphere can
contain at most one coronal hole. (2) Coronal holes of nested polarity regions
must themselves be nested. Magnetic reconnection plays the central role in
enforcing these constraints on the field topology. From these conjectures we
derive additional properties for the topology of open field regions, and
propose several observational predictions for both the slowly varying and
transient corona/solar wind.
