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 $\\mathbb{C}$ 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 $\\mathscr{L}(X,Y)$ between vector spaces $X, Y$ are rigid in the sense that any $L\\in\\mathscr{L}(X,Y)$ is completelydetermined by its values on any set of basis vectors of $X$ .
4.
Mostow’s rigidity theorem

单词	Rigid
释义	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 $\\mathbb{C}$ 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 $\\mathscr{L}(X,Y)$ between vector spaces $X, Y$ are rigid in the sense that any $L\\in\\mathscr{L}(X,Y)$ is completelydetermined by its values on any set of basis vectors of $X$ . 4. Mostow’s rigidity theorem
随便看	locally finite collection LocallyFiniteGraph locally finite graph LocallyFiniteGroup locally finite group LocallyFinitePoset locally finite poset LocallyFiniteQuiver locally finite quiver LocallyFree locally free LocallyHomeomorphic locally homeomorphic LocallyIntegrableFunction locally integrable function LocallyMaximal locally maximal LocallyNilpotentGroup locally nilpotent group LocallyRingedSpace locally ringed space LocallySimplyConnected locally simply connected LocallyTestable locally testable