Open AccessOn the Existence of $C^1$ Functions with Perfect Level Sets
Author(s) -
Emma DʼAniello,
Udayan B. Darji
Publication year - 2000
Publication title -
zeitschrift für analysis und ihre anwendungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.567
H-Index - 35
eISSN - 1661-4534
pISSN - 0232-2064
DOI - 10.4171/zaa/983
Subject(s) - mathematics , computer science , combinatorics , pure mathematics
Given a closed set M ⊂ [0, 1] of Lebesgue measure zero, we construct a C function f with the property that f−1({y}) is a perfect set for every y in M .
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom