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A
theorem on one-to-one mappings
Edwin Duda |
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Vol. 19 (1966), No. 2, 253–257
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Abstract |
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Let X be a locally connected generalized continuum with the property that the complement of each compact set has only one nonconditionally compact component. The author proves the following theorem. If f is a one-to-one mapping of X onto Euclidean 2-space, then f is a homeomorphism. An example of K. Whyburn implies that if f is a one-to-one mapping of X onto Euclidean n-space (n ≧ 3), then X can have many nice properties any yet f need not be a homeomorphism. However the complement of a compact set in the domain space of his example may have more than one nonconditionally compact component. It is interesting to note that a characterization of closed 2-cells in the plane is obtained in the course of proving the theorem. |
Mathematical Subject Classification
Primary: 54.60
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Milestones
Received: 6 August 1965
Published: 1 November 1966
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Authors |
| Edwin Duda | |
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