INTERSECTION OF CONTINUA AND RECTIFIABLE CURVES

被引：2
|
作者：
Balka, Richard [1 ]
Harangi, Viktor [1 ]
机构：
[1] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1364 Budapest, Hungary
来源：
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2014年 / 57卷 / 02期
基金：
匈牙利科学研究基金会;
关键词：
continuum; rectifiable curve; Hausdorff dimension;
D O I：
10.1017/S0013091513000527
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that for any non-degenerate continuum K subset of R-d there exists a rectifiable curve such that its intersection with K has Hausdorff dimension 1. This answers a question of Kirchheim.
引用
收藏
页码：339 / 345
页数：7
相关论文
共 50 条
  • [11] Hyperspaces of continua with connected boundaries in π-Euclidean Peano continua
    Krupski, Pawel
    TOPOLOGY AND ITS APPLICATIONS, 2020, 270
  • [12] Gate continua, absolute terminal continua and absolute retracts
    Charatonik, JJ
    Charatonik, WJ
    Prajs, JR
    HOUSTON JOURNAL OF MATHEMATICS, 2002, 28 (01): : 89 - 117
  • [13] On blockers in continua
    Bobok, Jozef
    Pyrih, Pavel
    Vejnar, Benjamin
    TOPOLOGY AND ITS APPLICATIONS, 2016, 202 : 346 - 355
  • [14] CONTINUOUSLY RAY EXTENDIBLE CONTINUA AND CIRCLE-LIKE CONTINUA
    Proctor, C. Wayne
    HOUSTON JOURNAL OF MATHEMATICS, 2010, 36 (04): : 1243 - 1323
  • [15] A Gromov’s dimension comparison estimate for rectifiable sets
    Valentino Magnani
    Aleksandra Zapadinskaya
    Selecta Mathematica, 2017, 23 : 1153 - 1174
  • [16] Non-rectifiable limit sets of dimension one
    Bishop, CJ
    REVISTA MATEMATICA IBEROAMERICANA, 2002, 18 (03) : 653 - 684
  • [17] A Gromov's dimension comparison estimate for rectifiable sets
    Magnani, Valentino
    Zapadinskaya, Aleksandra
    SELECTA MATHEMATICA-NEW SERIES, 2017, 23 (02): : 1153 - 1174
  • [18] Hereditarily non-weakly chainable continua in products of plane continua
    Illanes, Alejandro
    FUNDAMENTA MATHEMATICAE, 2017, 239 (01) : 19 - 27
  • [19] Continua with unique hyperspace
    Acosta, G
    CONTINUUM THEORY, 2002, 230 : 33 - 49
  • [20] CLASSIFYING HOMOGENEOUS CONTINUA
    ROGERS, JT
    TOPOLOGY AND ITS APPLICATIONS, 1992, 44 (1-3) : 341 - 352
12345