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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Burgess's theorem and related problems


Authors: Hisao Kato and Xiangdong Ye
Journal: Proc. Amer. Math. Soc. 128 (2000), 2501-2506
MSC (1991): Primary 54B15, 54F15, 54F50
Published electronically: February 25, 2000
MathSciNet review: 1653402
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Abstract: Let $G$ be a graph. We determine all graphs which are $G$-like. We also prove that if $G_{i}\ (i=1,2,\ldots , m)$ are graphs, then in order that each $G_{i}$-like $(i=1,2,\ldots , m)$ continuum $M$ be $n$-indecomposable for some $n=n(M)$ it is necessary and sufficient that if $K$ is a graph, then $K$ is not $G_{i}$-like for some integer $i$ with $1\le i\le m$. This generalizes a well known theorem of Burgess.


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Additional Information

Hisao Kato
Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba-Shi Ibaraki, 305, Japan
Email: hisakato@sakura.cc.tsukuba.ac.jp

Xiangdong Ye
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China
Email: yexd@math.ustc.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05247-3
PII: S 0002-9939(00)05247-3
Keywords: Graph, $n$-indecomposable, $\epsilon$-map, Burgess's theorem
Received by editor(s): March 24, 1998
Received by editor(s) in revised form: September 17, 1998
Published electronically: February 25, 2000
Additional Notes: This project was supported by NSFC 19625103 and JSPS of Japan.
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society