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The goal of this work is the development of the novel concept of “topological correlation” that compares two continuous functions f and g on a common manifold M. Assuming f and g are smooth, we define k(f,g) as the integral, over all points x on M, of the absolute size of the wedge product between the two gradients of f and g of x. This quantify may be interpreted as the size of the projection of M to the plane using f and g as the two coordinates. In the piecewise linear case, the integral is replaced by a sum. The topological correlation is defined as t(f,g) = l/(l+k(f,g)). We proved various algebraic properties of k and t and showed that they are sensitive to the critical point structure of f and g. In other words, they measure to what extent the critical structure of f resembles that of g. We also developed local versions of f and g and used them to visualize the change of a time-varying function.