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

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

... To say that a

**Cauchy Filter**s... 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 ...Uniform Space - Completeness

... Instead of working with

... Instead of working with

**Cauchy**sequences, one works with**Cauchy filters**(or**Cauchy**nets) ... A**Cauchy filter**F on a uniform space X is a**filter**F such that for every entourage U, there exists A∈F with A×A ⊆ U ... In other words, a**filter**is**Cauchy**if it contains "arbitrarily small" sets ...Cauchy Space

... In general topology and analysis, a

... In general topology and analysis, a

**Cauchy**space is a generalization of metric spaces and uniform spaces for which the notion of**Cauchy**convergence still makes sense ...**Cauchy**spaces were introduced by H ... Keller in 1968, as an axiomatic tool derived from the idea of a**Cauchy filter**, in order to study completeness in topological spaces ...Main Site Subjects

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