On the Theory of Structures in Sets

In many branches of mathematics the property of being a subspace receives considerable attention. The subspaces of a given space might be regarded as values of a structure in a set, that is, a function P on the subsets of a set V such that P(X) ⊆ V for all X ⊆ V. Thus, structures in sets form a basis for an abstract treatment of the property of being a subspace.