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Universality of the μ-predictor

Christopher S. Hardin (2013)

Fundamenta Mathematicae

For suitable topological spaces X and Y, given a continuous function f:X → Y and a point x ∈ X, one can determine the value of f(x) from the values of f on a deleted neighborhood of x by taking the limit of f. If f is not required to be continuous, it is impossible to determine f(x) from this information (provided |Y| ≥ 2), but as the author and Alan Taylor showed in 2009, there is nevertheless a means of guessing f(x), called the μ-predictor, that will be correct except on a small set; specifically,...

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