The general theory of radicals was defined independently by and .

The same identifier can be independently defined in multiple namespaces.

Furthermore, the categories are defined independently of the set of alternatives under consideration.

Since the 18th century Asia has been divided into several subregions independently defined from Asia as a whole.

Intuitively, it is not "consistently defined independently of dimension".

In particular h and the g are defined independently of any algorithm to compute them.

Unlike debates sponsored at the high school or collegiate level, the participants, format, and rules are not independently defined.

Unlike the pre-1971 roentgen, the gray has always been defined independently of any target material.

Sets cannot be independently defined by any arbitrary logically definable notion.

The research group chooses the documents to be published according to independently defined criteria and is only bound to scientific principles.