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First Return Approachability

✍ Scribed by Udayan B. Darji; Michael J. Evans; Paul D. Humke

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
181 KB
Volume
199
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

We consider real-valued functions defined on 0, 1 . Both the class of Baire one functions and the class of Baire-one, Darboux functions have been characterized using first return limit notions. The former class consists of the first return recoverable functions and the latter consists of the first return continuous functions. Here we introduce a natural intermediate type of first return limiting process, first return approachability, and show that the first return approachable functions are precisely those Baire class one functions whose graphs are dense in themselves. Also, the set of points at which a function is first return approachable, but not first return continuous, is shown to be -porous.

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