Limit-like predictability for discontinuous functions

Authors:
Christopher S. Hardin and Alan D. Taylor

Journal:
Proc. Amer. Math. Soc. **137** (2009), 3123-3128

MSC (2000):
Primary 03E05; Secondary 54H05, 54C99

Published electronically:
March 18, 2009

MathSciNet review:
2506471

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Abstract | References | Similar Articles | Additional Information

Abstract: Our starting point is the following question: To what extent is a function's value at a point of a topological space determined by its values in an arbitrarily small (deleted) neighborhood of ? For continuous functions, the answer is typically ``always'' and the method of prediction of is just the limit operator. We generalize this to the case of an arbitrary function mapping a topological space to an arbitrary set. We show that the best one can ever hope to do is to predict correctly except on a scattered set. Moreover, we give a predictor whose error set, in spaces, is always scattered.

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Additional Information

**Christopher S. Hardin**

Affiliation:
Department of Mathematics and Computer Science, Wabash College, Crawfordsville, Indiana 47933

Email:
hardinc@wabash.edu

**Alan D. Taylor**

Affiliation:
Department of Mathematics, Union College, Schenectady, New York 12308

Email:
taylora@union.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-09-09877-3

Keywords:
Scattered sets

Received by editor(s):
June 9, 2008

Received by editor(s) in revised form:
January 9, 2009

Published electronically:
March 18, 2009

Communicated by:
Julia Knight

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.