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 $c$ than one would expect.
It should be emphasized that the above “definition” does not define a mathematical object. Instead, it describes in what sense the 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 that they are uniquely determined by their boundary values.

2.
By the fundamental theorem of algebra^{}, polynomials^{} in $\u2102$ are rigid in the sense that any polynomial is completely determined by its values on any countably infinite^{} set, say $\mathbb{N}$, or the unit disk.

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

4.
Mostow’s rigidity theorem
Title  rigid 

Canonical name  Rigid 
Date of creation  20130322 14:38:10 
Last modified on  20130322 14:38:10 
Owner  matte (1858) 
Last modified by  matte (1858) 
Numerical id  11 
Author  matte (1858) 
Entry type  Definition 
Classification  msc 0001 
Synonym  rigidity result 
Synonym  rigidity theorem 
Synonym  rigidity 