Abstract
If x and y are two points of a compact metric space E , we call connectivity in E between x and y the smallest number of points other than x or y that we must withdraw from E in order to get a metric space which does not admit any continuous path between x and y . We denote this number by C E ( x , y ) and we prove, under some regularity conditions on E , that if C E ( x , y ) < ∞, then there exists in E a system of C E ( x , y ) innerly disjoint continuous paths between x and y . This result provides us with an extension of Menger's theorem for finite graphs and we show how it may become incorrect when E presents some kinds of irregularities.
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