Menger curves in Peano continua
P. Krupski, H. Patkowska (1996)
Colloquium Mathematicae
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P. Krupski, H. Patkowska (1996)
Colloquium Mathematicae
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Janusz Jerzy Charatonik, Paweł Krupski (2002)
Commentationes Mathematicae Universitatis Carolinae
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It is shown that for every numbers there is a strongly self-homeomorphic dendrite which is not pointwise self-homeomorphic. The set of all points at which the dendrite is pointwise self-homeomorphic is characterized. A general method of constructing a large family of dendrites with the same property is presented.
Alejandro Illanes (1998)
Colloquium Mathematicae
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Kazuhiro Kawamura (1991)
Colloquium Mathematicae
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A continuum means a compact connected metric space. For a continuum X, H(X) denotes the space of all homeomorphisms of X with the compact-open topology. It is well known that H(X) is a completely metrizable, separable topological group. J. Kennedy [8] considered a compactification of H(X) and studied its properties when X has various types of homogeneity. In this paper we are concerned with the compactification of the homeomorphism group of the pseudo-arc P, which is obtained by the...
Hanna Patkowska (1993)
Fundamenta Mathematicae
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A space X containing a Cantor set (an arc) is Cantor (arcwise) homogeneousiff for any two Cantor sets (arcs) A,B ⊂ X there is an autohomeomorphism h of X such that h(A)=B. It is proved that a continuum (an arcwise connected continuum) X such that either dim X=1 or is Cantor (arcwise) homogeneous iff X is a closed manifold of dimension at most 2.
Carter, Sheila, Craveiro de Carvalho, F.J. (2005)
Beiträge zur Algebra und Geometrie
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J. Nymann (1995)
Colloquium Mathematicae
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Kennedy, Judy (2003)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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