Such relations between species of spaces may be expressed diagrammatically as shown in Fig. 3. An arrow from A to B means that every is also a or may be treated as a or provides a etc. Treating A and B as classes of spaces one may interpret the arrow as a transition from A to B. (In Bourbaki's terms, "procedure of deduction" of a from a Not quite a function unless the classes A,B are sets; this nuance does not invalidate the following.) The two arrows on Fig. 3 are not invertible, but for different reasons.