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# Homogeneous Suslinian Continua

Published:2011-01-26
Printed: Jun 2011
• D. Daniel,
Lamar University, Department of Mathematics, Beaumont, TX, U.S.A.
• J. Nikiel,
Opole University, Institute of Mathematics and Informatics, Opole, Poland
• L. B. Treybig,
Texas A&M University, Department of Mathematics, College Station, TX, U.S.A.
• H. M. Tuncali,
Nipissing University, Faculty of Arts and Sciences, North Bay, ON
• E. D. Tymchatyn,
A continuum is 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.
 MSC Classifications: 54F15 - Continua and generalizations 54C05 - Continuous maps 54F05 - Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30] 54F50 - Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03]