The co-image of a mapping is the subset of the domain for which the mapping returns something. For example, the Pet-Of mapping from humans to animals will have an subtype of humans that own pets at any given time, namely Pet-Owner, which is the co-image. Whereas the domain gives the inputs that possibly have results, the co-image gives the inputs that actually have results. The co-image may be the same as the domain. The image of a mapping is the subset of the range which the mapping actually returns as output. For example, the Pet-Of mapping from humans to animals will have an subtype of animals that are pets at any given time, namely Pet, which is the image. Whereas the range gives the possible results of the mappings, the image gives the actual results. If the image is the same as the range, the mapping is said to be "onto" or "surjective"; otherwise it is called "into". Since mappings always return sets, to accommodate multiple-values and no-values, it is more exact to say that the co-image is the subset of the domain which maps to a non-empty set. The three techniques for modelling images also apply to co-images (see hasImage/isImageOf), substituting Pet-Owner for Pet, and domain for range. See Place Relation for discussion of the similarities and differences between images and role types. See the summary with example at Place Relation.