On the rim-types of hereditarily locally connected continua
E. Tymchatyn (1975)
Fundamenta Mathematicae
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E. Tymchatyn (1975)
Fundamenta Mathematicae
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T. Maćkowiak, E. D. Tymchatyn (1987)
Colloquium Mathematicae
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Mirosława Reńska (2011)
Colloquium Mathematicae
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We show that a metrizable continuum X is locally connected if and only if every partition in the cylinder over X between the bottom and the top of the cylinder contains a connected partition between these sets. J. Krasinkiewicz asked whether for every metrizable continuum X there exists a partiton L between the top and the bottom of the cylinder X × I such that L is a hereditarily indecomposable continuum. We answer this question in the negative. We also present a...
Udayan B. Darji, Alberto Marcone (2004)
Fundamenta Mathematicae
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We show that each of the classes of hereditarily locally connected, finitely Suslinian, and Suslinian continua is Π₁¹-complete, while the class of regular continua is Π₀⁴-complete.
Joseph N. Simone (1978)
Colloquium Mathematicae
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T. Maćkowiak (1987)
Colloquium Mathematicae
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Alejandro Illanes (1998)
Commentationes Mathematicae Universitatis Carolinae
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A retractible non-locally connected dendroid is constructed.
Joseph N. Simone (1978)
Colloquium Mathematicae
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L. Mohler (1970)
Colloquium Mathematicae
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S. Drobot (1971)
Applicationes Mathematicae
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Lončar, Ivan (2008)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Jerzy Krzempek (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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It is shown that a certain indecomposable chainable continuum is the domain of an exactly two-to-one continuous map. This answers a question of Jo W. Heath.
Hisao Kato (1988)
Fundamenta Mathematicae
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