The edges of channels etched into topographically patterned substrates impart orientational order to rnonolayers of poly(styrene-b-2-vinylpyridine) cylinders. Quantitative measures of orientational order as well as defect densities are presented for cylinder arrays confined in channels of width varying between 1 and 3 mu m, with little, if any, difference observed between these different channel widths. As the temperature is raised, the cylinder monolayers underao a nematic-to-isotropic disordering transition. However. above this transition temperature, orientational order is retained within several cylinder repeat spacings next to the channel edges (distances significantly less than the channel widths considered here). This effect arises from an effective repulsion of defects from those edges, as confirmed by position-dependent defect density measurements.