# Exponential law

From Encyclopedia of Mathematics

A term with a variety of meanings.

A process which changes by a fixed factor over a fixed time period: exponential growth or decay.

A property of the exponential function, such as $\exp(x+y) = \exp(x)\exp(y)$ or of a power, such as $x^{yz} = (x^y)^z$.

A property of sets of maps between sets, such as $\mathrm{Map}(X\times Y,Z) \leftrightarrow \mathrm{Map}(X, \mathrm{Map}(Y,Z))$, see Exponential law for sets.

A property of sets of continuous maps between topological spaces, see Exponential law (in topology).

**How to Cite This Entry:**

Exponential law.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Exponential_law&oldid=35708