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, if X is T₀, then the guesses will be correct except on a scattered set. In this paper, we show that, when X is T₀, every predictor that performs this well is a special case of the μ-predictor.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-3-4,
author = {Christopher S. Hardin},
title = {Universality of the $\mu$-predictor},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {227-241},
zbl = {1273.03148},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-3-4}
}
Christopher S. Hardin. Universality of the μ-predictor. Fundamenta Mathematicae, Tome 220 (2013) pp. 227-241. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-3-4/