### Some articles on *cauchy filters, filter, cauchy, cauchy filter*:

Filter (mathematics) - Filter On A Set - Filters in Topology -

... To say that a

**Cauchy Filters**... To say that a

**filter**base B on X is**Cauchy**means that for each real number ε>0, there is a B0 ∈ B such that the metric diameter of B0 is less than ε ... (xn) is a**Cauchy**sequence if and only if the**filter**base {{xN,xN+1...} N ∈ {1,2,3...} } is**Cauchy**... More generally, given a uniform space X, a**filter**F on X is called**Cauchy filter**if for every entourage U there is an A ∈ F with (x,y) ∈ U for all x,y ∈ A ...### Famous quotes containing the word filters:

“Raise a million *filters* and the rain will not be clean, until the longing for it be refined in deep confession. And still we hear, If only this nation had a soul, or, Let us change the way we trade, or, Let us be proud of our region.”

—Leonard Cohen (b. 1934)

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