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 $ϵ\mathrm{>}\mathrm{0}$ there exists $X\mathrm{\in }B$ such that the oscillation of $f$ on $X$ is less than $ϵ$.

For a proof of this theorem see[1].

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