  Models for the origin of the slow solar wind must account for two seemingly
contradictory observations: The slow wind has the composition of the closed
field corona, implying that it originates from the continuous opening and
closing of flux at the boundary between open and closed field. On the other
hand, the slow wind also has large angular width, up to ~ 60{\circ}, suggesting
that its source extends far from the open-closed boundary. We propose a model
that can explain both observations. The key idea is that the source of the slow
wind at the Sun is a network of narrow (possibly singular) open-field corridors
that map to a web of separatrices and quasi-separatrix layers in the
heliosphere. We compute analytically the topology of an open-field corridor and
show that it produces a quasi-separatrix layer in the heliosphere that extends
to angles far from the heliospheric current sheet. We then use an MHD code and
MDI/SOHO observations of the photospheric magnetic field to calculate
numerically, with high spatial resolution, the quasi-steady solar wind and
magnetic field for a time period preceding the August 1, 2008 total solar
eclipse. Our numerical results imply that, at least for this time period, a web
of separatrices (which we term an S-web) forms with sufficient density and
extent in the heliosphere to account for the observed properties of the slow
wind. We discuss the implications of our S-web model for the structure and
dynamics of the corona and heliosphere, and propose further tests of the model.
