Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A characterization of $ \sigma$-symmetrically porous symmetric Cantor sets


Authors: Michael J. Evans, Paul D. Humke and Karen Saxe
Journal: Proc. Amer. Math. Soc. 122 (1994), 805-810
MSC: Primary 26A03
DOI: https://doi.org/10.1090/S0002-9939-1994-1205490-X
MathSciNet review: 1205490
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is to characterize those symmetric Cantor sets which are $ \sigma $-symmetrically porous in terms of a defining sequence of deleted proportions. In contrast to other notions of porosity, a symmetric Cantor set can be $ \sigma $-symmetrically porous without being symmetrically porous.


References [Enhancements On Off] (What's this?)

  • [1] C. L. Belna, M. J. Evans, and P. D. Humke, Symmetric and ordinary differentiation, Proc. Amer. Math. Soc. 72 (1978), 261-267. MR 507319 (80d:26006)
  • [2] M. J. Evans, Some theorems whose $ \sigma $-porous exceptional sets are not $ \sigma $-symmetrically porous, Real Anal. Exchange 17 (1991-92), 809-814. MR 1171425 (94b:26008b)
  • [3] -, A note on symmetric and ordinary differentiation, Real Anal. Exchange 17 (1991-92), 820-826. MR 1171427 (94b:26008a)
  • [4] M. J. Evans, P. D. Humke, and K. Saxe, A symmetric porosity conjecture of L. Zajíček, Real Anal. Exchange 17 (1991-92), 258-271. MR 1147367 (93g:26019)
  • [5] -, Symmetric porosity of symmetric Cantor sets, Czech. Math. J. (to appear).
  • [6] P. D. Humke, A criterion for the nonporosity of a general Cantor set, Proc. Amer. Math. Soc. 111 (1991), 365-372. MR 1039532 (91f:26004)
  • [7] P. D. Humke and B. S. Thomson, A porosity characterization of symmetric perfect sets, Classical Real Analysis, Contemp. Math., vol. 42, Amer. Math. Soc., Providence, RI, 1985, pp. 81-86. MR 807980 (86m:26004)
  • [8] M. Repický, An example which discerns porosity and symmetric porosity, Real Anal. Exchange 17 (1991-92), 416-420. MR 1147383 (93b:26001)
  • [9] L. Zajíček, Porosity and $ \sigma $-porosity, Real Anal. Exchange 13 (1987-88), 314-350. MR 943561 (89e:26009)
  • [10] -, A note on the symmetric and ordinary derivative, preprint.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A03

Retrieve articles in all journals with MSC: 26A03


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1205490-X
Keywords: Cantor set, symmetric porous
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society