Displaying similar documents to “A C -continuum x is metrizable if and only if it admits a Whitney map for C ( x ) .”

Four mapping problems of Maćkowiak

E. Grace, E. Vought (1996)

Colloquium Mathematicae

Similarity:

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

Similarity:

The body of this paper falls into two independent sections. The first deals with the existence of cross-sections in F σ -decompositions. The second deals with the extensions of the results on accessibility in the plane.

Hereditarily weakly confluent induced mappings are homeomorphisms

Janusz Charatonik, Włodzimierz Charatonik (1998)

Colloquium Mathematicae

Similarity:

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. ...