A -continuum is metrizable if and only if it admits a Whitney map for .
Lončar, Ivan (2009)
Acta Universitatis Apulensis. Mathematics - Informatics
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Lončar, Ivan (2009)
Acta Universitatis Apulensis. Mathematics - Informatics
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E. Grace, E. Vought (1996)
Colloquium Mathematicae
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In his paper "Continuous mappings on continua" [5], T. Maćkowiak collected results concerning mappings on metric continua. These results are theorems, counterexamples, and unsolved problems and are listed in a series of tables at the ends of chapters. It is the purpose of the present paper to provide solutions (three proofs and one example) to four of those problems.
Janusz Charatonik, Włodzimierz Charatonik (1998)
Colloquium Mathematicae
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For a given mapping f between continua we consider the induced mappings between the corresponding hyperspaces of closed subsets or of subcontinua. It is shown that if either of the two induced mappings is hereditarily weakly confluent (or hereditarily confluent, or hereditarily monotone, or atomic), then f is a homeomorphism, and consequently so are both the induced mappings. Similar results are obtained for mappings between cones over the domain and over the range continua. ...
Kennedy, Judy (2003)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Wojciech Dębski, E. Tymchatyn (1991)
Fundamenta Mathematicae
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The body of this paper falls into two independent sections. The first deals with the existence of cross-sections in -decompositions. The second deals with the extensions of the results on accessibility in the plane.
R. Ayala, M. Chávez, A. Quintero (1998)
Colloquium Mathematicae
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We extend a theorem of S. Claytor in order to characterize the Peano generalized continua which are embeddable into the 2-sphere. We also give a characterization of the Peano generalized continua which admit closed embeddings in the Euclidean plane.
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...
P. Krupski, H. Patkowska (1996)
Colloquium Mathematicae
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Alejandro Illanes (1998)
Colloquium Mathematicae
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