Self-similarity
Self-similarity has been treated recently in connection with the study of fractals; so the paper seems to be very actual. In Section 1 a self- similar set is defined as a compact set which is the union of its images under members of a collection of contractions (indexed by a compact set) having a common contradictivity factor. In Section 2 self-similarity is characterized ``addressing'' or considering points in the self-similar set as limits associated with certain sequences of contractions. The existence of self-similar sets determined by a collection of a certain type of contractions is proved in Section 3. A self-similar set is treated in Section 4 as a fixed point in hyperspaces and the continuous variation of self-similar sets is shown in the last Section 5. In the Introduction a short historical review is presented.
scientific article; zbMATH DE number 515171
scientific article