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Hereditarily weakly confluent induced mappings are homeomorphisms

Janusz Charatonik, Włodzimierz Charatonik (1998)

Colloquium Mathematicae

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.

Homotopy properties of curves

Janusz Jerzy Charatonik, Alejandro Illanes (1998)

Commentationes Mathematicae Universitatis Carolinae

Conditions are investigated that imply noncontractibility of curves. In particular, a plane noncontractible dendroid is constructed which contains no homotopically fixed subset. A new concept of a homotopically steady subset of a space is introduced and its connections with other related concepts are studied.

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