Geodesic
Homogeneous Suslinian Continua
Canadian mathematical bulletin, Tome 54 (2011) no. 2, pp. 244-248

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DOI

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.
DOI : 10.4153/CMB-2011-001-8
Mots-clés : 54F15, 54C05, 54F05, 54F50, connected im kleinen, homogeneity, Suslinian, locally connected continuum 
Daniel, D.; Nikiel, J.; Treybig, L. B.; Tuncali, H. M.; Tymchatyn, E. D. Homogeneous Suslinian Continua. Canadian mathematical bulletin, Tome 54 (2011) no. 2, pp. 244-248. doi: 10.4153/CMB-2011-001-8
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     title = {Homogeneous {Suslinian} {Continua}},
     journal = {Canadian mathematical bulletin},
     pages = {244--248},
     year = {2011},
     volume = {54},
     number = {2},
     doi = {10.4153/CMB-2011-001-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-001-8/}
}
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