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Homogeneous Suslinian Continua

Published online by Cambridge University Press:  20 November 2018

D. Daniel ,
J. Nikiel ,
L. B. Treybig ,
H. M. Tuncali  and
E. D. Tymchatyn
D. Daniel
Affiliation:
Lamar University, Department of Mathematics, Beaumont, TX, U.S.A.e-mail: dale.daniel@lamar.edu
J. Nikiel
Affiliation:
Opole University, Institute of Mathematics and Informatics, Opole, Polande-mail: nikiel@math.uni.opole.pl
L. B. Treybig
Affiliation:
Texas A&M University, Department of Mathematics, College Station, TX, U.S.A.e-mail: muratt@nipissingu.ca
H. M. Tuncali
Affiliation:
Nipissing University, Faculty of Arts and Sciences, North Bay, ONe-mail: tymchat@snoopy.usask.ca
E. D. Tymchatyn
Affiliation:
University of Saskatchewan, Department of Mathematics, Saskatoon, SK
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Abstract

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A continuumis said to be Suslinian if it does not contain uncountably many mutually exclusive non-degenerate subcontinua. Fitzpatrick and Lelek have shown that a metric Suslinian continuum $X$ has the property that the set of points at which $X$ is connected im kleinen is dense in $X$. We extend their result to Hausdorff Suslinian continua and obtain a number of corollaries. In particular, we prove that a homogeneous, non-degenerate, Suslinian continuum is a simple closed curve and that each separable, non-degenerate, homogenous, Suslinian continuum is metrizable.

Keywords

54F1554C0554F0554F50connected im kleinenhomogeneitySuslinianlocally connected continuum
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 2 , 01 June 2011 , pp. 244 - 248
Copyright
Copyright © Canadian Mathematical Society 2011

References

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