Recent research in hyperspace theory.
Janusz J. Charatonik (2003)
Extracta Mathematicae
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Displaying similar documents to “A -continuum is metrizable if and only if it admits a Whitney map for .”
Recent research in hyperspace theory.
Four mapping problems of Maćkowiak
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.
Composant-like decompositions
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.
More on the shift dynamics-indecomposable continua connection.
Kennedy, Judy (2003)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Weight and metrizability of inverses under hereditarily irreducible mappings.
Lončar, Ivan (2008)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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On the planarity of Peano generalized continua: An extension of a theorem of S. Claytor
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.
Hereditarily weakly confluent induced mappings are homeomorphisms
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. ...
On composants of Hausdorff continua
M. Proffitt (1971)
Fundamenta Mathematicae
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