1. Where are typical C1 functions one-to-one?
- Creator:
- Buczolich, Zoltán and Máthé, András
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- typical function, box dimension, and one-to-one function
- Language:
- English
- Description:
- Suppose F ⊂ [0, 1] is closed. Is it true that the typical (in the sense of Baire category) function in C 1 [0, 1] is one-to-one on F? If dimBF < 1/2 we show that the answer to this question is yes, though we construct an F with dimB F = 1/2 for which the answer is no. If Cα is the middle-α Cantor set we prove that the answer is yes if and only if dim(Cα) ≤ 1/2. There are F’s with Hausdorff dimension one for which the answer is still yes. Some other related results are also presented.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public