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.
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