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Hometopological divisor of zero
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topological divisor of zero
Let $A$ be a normed ring. An element $a\in A$ is said to be a left topological divisor of zero if there is a sequence $a_{n}$ with $\a_{n}\=1$ for all $n$ such that
$\lim_{{n\to\infty}}\aa_{n}\=0.$ 
Analogously, $a$ is a right topological divisor of zero if
$\lim_{{n\to\infty}}\b_{n}a\=0,$ 
for some sequence $b_{n}$ with $\b_{n}\=1$. The element $a$ is a topological divisor of zero if it is both a left and a right topological divisor of zero.
Remarks.

Any zero divisor is a topological divisor of zero.

In a commutative Banach algebra $A$, an element is a topological divisor of zero if it lies on the boundary of $U(A)$, the group of units of $A$.
Synonym:
generalized divisor of zero
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