SOME REMARKS ON THE DIMENSIONS OF THE PRODUCTS OF CANTOR SETS

• 발행기관: 충청수학회
• 저자명: Jin Oh Kim
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 23, No. 2, 231~236쪽, 전체 6쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2010.06.30

영문 초록

Using the properties of the concave function, we show that the Hausdor？？ dimension of the product Ca+b 2 ; a+b 2£Ca+b 2 ; a+b 2 of the same symmetric Cantor sets is greater than that of the prod-uct Ca;b £ Ca;b of the same anti-symmetric Cantor sets. Further, for 1=e2 < a; b < 1=2, we also show that the dimension of the prod-uct Ca;a £ Cb;b of the di？？erent symmetric Cantor sets is greater than that of the product Ca+b 2 ; a+b 2 £ Ca+b 2 ; a+b of the same sym- metric Cantor sets using the concavity. Finally we give a concrete example showing that the latter argument does not hold for all 0 < a; b < 1=2.

목차

1. Introduction

2. Preliminaries

3. Main results

Acknowledgments

References