Let \(X\) be a topological space and \(I = [0,1]\). The space \(X\) is path connected if for every pair of points \(x\neq y\) in \(X\) there exists a path \(f\colon I \to X\) with \(f(0) = x\) and \(f(1) = y\).
Path-connected space
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Let \(X\) be a topological space and \(I = [0,1]\). The space \(X\) is path connected if for every pair of points \(x\neq y\) in \(X\) there exists a path \(f\colon I \to X\) with \(f(0) = x\) and \(f(1) = y\).