Universality of the μ-predictor

Christopher S. Hardin. "Universality of the μ-predictor." Fundamenta Mathematicae 220.3 (2013): 227-241. <http://eudml.org/doc/283332>.

@article{ChristopherS2013,
abstract = {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.},
author = {Christopher S. Hardin},
journal = {Fundamenta Mathematicae},
keywords = {-predictor; scattered sets; weakly scattered sets; well-orderings},
language = {eng},
number = {3},
pages = {227-241},
title = {Universality of the μ-predictor},
url = {http://eudml.org/doc/283332},
volume = {220},
year = {2013},
}

TY - JOUR
AU - Christopher S. Hardin
TI - Universality of the μ-predictor
JO - Fundamenta Mathematicae
PY - 2013
VL - 220
IS - 3
SP - 227
EP - 241
AB - 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.
LA - eng
KW - -predictor; scattered sets; weakly scattered sets; well-orderings
UR - http://eudml.org/doc/283332
ER -