Example 1

\* The species of topological group structures has a single principal base set $A$, no auxiliary base set, and the corresponding generic structure is a pair $(s_1,s_2)$ ($s_1$ being the graph of the law of composition on $A$, and $s_2$ the set of open sets in the topology of $A$; cf. General Topology, Chapter III, § 1). Each of the terms $s_1,s_2$ is a procedure of deduction and provides respectively the group structure and the topology underlying the topological group structure $(s_1,s_2)$.

Likewise, from a vector space structure can be deduced an underlying commutative group structure. From a ring structure can be deduced an underlying commutative group structure and a (multiplicative) semigroup

IV STRUCTURES

structure. From the structure of a differentiable manifold can be deduced an underlying topology, etc.