Institutional Repository
Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/ADF56840-C61F-4EA1-96E5-83E78CE3609B | ||
| Year | 1978 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
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| Bibliographic Citation | J. Grispolakis and E.D. Tymchatyn, "Continua which admit only certain classes of onto mappings", Topology Proceedings, vol. 3, pp. 347-362, 1978. | ||
| Appears in Collections |
The purpose of this article is to present a rather com plete study of those classes of continua which admit only confluent (resp. semi-confluent, weakly confluent, pseudo-confluent) onto mappings. The first results were obtained by H. Cook [3] who proved that if X is a hereditarily inde composable continuum, then every mapping from any continuum onto X is confluent, and by D. R. Read [20] who proved that the converse is true, that is, if X is a continuum such that every mapping from any continuum onto X is confluent, then X is hereditarily indecomposable. In what follows we study the class of continua X with the property that every mapping from any continuum onto X is weakly confluent. Finally, at the end of the paper we study the classes of continua X with the property that every mapping from any continuum onto X is semi-confluent (resp., pseudo-confluent>. 1. Definitions and Preliminaries By a continuum is meant a connected, compact, metric space. By a mapping is always meant a continuous function. A mapping f: X ~ Y of a continuum X onto a continuum Y is said to be confluent [2], semi-confluent [18], or weakly lThe first author was supported by a University of Saskatchewan postdoctoral fellowship.
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