rigid

Suppose $C$ is a collection of mathematical objects(for instance, sets, or functions).Then we say that $C$ is rigid if every $c\in C$is uniquely determined by less information about $c$ thanone would expect.

It should be emphasized that the above “definition” does notdefine a mathematical object. Instead, it describes in what sensethe adjective rigid is typically used in mathematics,by mathematicians.

Let us illustrate this by some examples:

1. Harmonic functions on the unit disk are rigid in the sense thatthey are uniquely determined by their boundary values.

2. By the fundamental theorem of algebra, polynomials in $ℂ$are rigid in the sense that any polynomial is completely determined byits values on any countably infinite set, say $\mathbb{N}$, or the unit disk.

3. Linear maps $ℒ(X,Y)$ between vector spaces $X,Y$are rigid in the sense that any $L\in ℒ(X,Y)$ is completelydetermined by its values on any set of basis vectors of $X$.

4. Mostow’s rigidity theorem