# Cauchy criterion for the existence of a limit of a function

###### Theorem 1.

Let $S$ be a set and $B$ a filter basis in $S$. A function $f:S\to\mathbb{R}$ possesses limit on $B$, iff for every $\epsilon>0$ there exists $X\in B$ such that the oscillation of $f$ on $X$ is less than $\epsilon$.

For a proof of this theorem see[1].

## References

• 1 V., Zorich, , pp. 132ff, First Ed., Springer-Verlag, 2004.
Title Cauchy criterion for the existence of a limit of a function CauchyCriterionForTheExistenceOfALimitOfAFunction 2013-03-22 17:45:52 2013-03-22 17:45:52 perucho (2192) perucho (2192) 6 perucho (2192) Theorem msc 26A06 CauchyConditionForLimitOfFunction