In mathematics, an element of a Banach algebra is called a topological divisor of zero if there exists a sequence of elements of such that
If such a sequence exists, then one may assume that for all .
If is not commutative, then is called a "left" topological divisor of zero, and one may define "right" topological divisors of zero similarly.
The notion of a topological divisor of zero may be generalized to any topological algebra. If the algebra in question is not first-countable, one must substitute nets for the sequences used in the definition.