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Definition: Given points x and y of the space X, a path in X from x to u is a continuous map f: [a, b] -> X of some closed interval in the real line into X, such that f(a) = x and f(b) = y. A space is said to be path connected if every pair of points of X can be joined by a path in X.
Source: Topology (second edition) by James R. Munkres