Universality of the μ-predictor

• Autorzy: Christopher S. Hardin
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E05: Other combinatorial set theory
• 54H99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 220
• Numer: 3
• Strony: 227-241

Daty

wydano

2013

Twórcy

autor

Christopher S. Hardin

• 1 New York Plaza, 33rd Floor, New York, NY 10004, U.S.A.

Identyfikatory

DOI

10.4064/fm220-3-4