Final answer:
Yes, if the universe had an edge, it would violate isotropy, a key aspect of the cosmological principle which posits that the universe is uniform in all directions.
Step-by-step explanation:
If the universe had an edge, it would indeed violate the assumption of isotropy which is a key part of the cosmological principle. Isotropy means the universe should appear the same in all directions from any given point. An edge would introduce a special direction and a boundary, which implies that the laws of physics or the appearance of the universe would somehow be different looking towards the edge as opposed to looking away from it.
This would contradict the cosmological principle that suggests the universe on the large scale is both isotropic and homogeneous, i.e., the same in every place and in every direction.
These core ideas are supported by a wealth of observational evidence. For example, the Automated Plate Measurement Galaxy Survey has contributed to the understanding of the universe's isotropy and homogeneity.
While the universe does exhibit local clumps in the form of galaxies and galaxy clusters, the overall homogeneity still stands when viewed on a sufficiently large scale. Additionally, the expansion of the universe is consistent with these principles - the expansion rate is the same everywhere based on current observations, and such uniformity further substantiates the cosmological principle.