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Existence of quasi-arcs
Author(s):
John
M.
Mackay
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3975-3981.
MSC (2000):
Primary 30C65;
Secondary 54D05
Posted:
June 5, 2008
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Abstract:
We show that doubling, linearly connected metric spaces are quasi-arc connected. This gives a new and short proof of a theorem of Tukia.
References:
-
- 1.
- M. Bonk and B. Kleiner, Quasi-hyperbolic planes in hyperbolic groups, Proc. Amer. Math. Soc. 133 (2005), no. 9, 2491-2494 (electronic). MR 2146190 (2005m:20098)
- 2.
- D. Burago, Y. Burago, and S. Ivanov, A course in metric geometry, Graduate Studies in Mathematics, vol. 33, American Mathematical Society, Providence, RI, 2001. MR 1835418 (2002e:53053)
- 3.
- H. F. Cullen, Introduction to general topology, D. C. Heath and Co., Boston, Mass., 1968. MR 0221455 (36:4507)
- 4.
- J. G. Hocking and G. S. Young, Topology, second ed., Dover Publications Inc., New York, 1988. MR 1016814 (90h:54001)
- 5.
- J. M. Mackay, Spaces with conformal dimension greater than one, preprint (2007), arXiv:0711.0417.
- 6.
- P. Tukia, Spaces and arcs of bounded turning, Michigan Math. J. 43 (1996), no. 3, 559-584. MR 1420592 (98a:30028)
- 7.
- P. Tukia and J. Väisälä, Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980), no. 1, 97-114. MR 595180 (82g:30038)
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Additional Information:
John
M.
Mackay
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
Address at time of publication:
Department of Mathematics, Yale University, New Haven, Connecticut 06520-8283
Email:
jmmackay@umich.edu
DOI:
10.1090/S0002-9939-08-09444-6
PII:
S 0002-9939(08)09444-6
Keywords:
Quasi-arc,
linearly connected,
bounded turning.
Received by editor(s):
October 17, 2007
Posted:
June 5, 2008
Additional Notes:
This research was partially supported by NSF grant DMS-0701515.
Communicated by:
Mario Bonk
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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