A characterization of -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 -symmetrically porous in terms of a defining sequence of deleted proportions. In contrast to other notions of porosity, a symmetric Cantor set can be -symmetrically porous without being symmetrically porous.

**[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*-*porous exceptional sets are not*-*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*-*porosity*, Real Anal. Exchange**13**(1987-88), 314-350. MR**943561 (89e:26009)****[10]**-,*A note on the symmetric and ordinary derivative*, preprint.

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