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Whitney maps-a non-metric case

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Charatonik J. J. , Charatonik W. J.

Colloquium Mathematicum

2000

tom 83

nr 2

305-307

It is shown that there is no Whitney map on the hyperspace $2^X$ for non-metrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X).

Hereditarily weakly confluent induced mappings are homeomorphisms

100%

Charatonik J. J. , Charatonik W. J.

Colloquium Mathematicum

1998

tom 75

nr 2

195-203

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.