# 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 $f\mathrm{:}S\mathrm{\to}\mathrm{R}$ possesses limit on $B$, iff for every $\u03f5\mathrm{>}\mathrm{0}$ there exists $X\mathrm{\in}B$ such that the oscillation of $f$ on $X$ is less than $\u03f5$.

## References

- 1 V., Zorich, Mathematical Analysis I, pp. 132ff, First Ed., Springer-Verlag, 2004.

Title | Cauchy criterion for the existence of a limit of a function |
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Canonical name | CauchyCriterionForTheExistenceOfALimitOfAFunction |

Date of creation | 2013-03-22 17:45:52 |

Last modified on | 2013-03-22 17:45:52 |

Owner | perucho (2192) |

Last modified by | perucho (2192) |

Numerical id | 6 |

Author | perucho (2192) |

Entry type | Theorem |

Classification | msc 26A06 |

Related topic | CauchyConditionForLimitOfFunction |