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Reflexive open mappings on generalized graphs

Part of: Maps and general types of spaces defined by maps Special properties

Published online by Cambridge University Press:  09 April 2009

Stanislaw Miklos
Stanislaw Miklos
Affiliation:
Institute of Mathematics University of Wroclawpl. Grunwaldzki 2/4 50–384 Wroclaw, Poland
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Abstract

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In this paper we show that a locally connected and locally compact metric image of a generalized graph under a reflexive open mapping is a generalized graph; further, we characterize all acyclic generalized graphs X with the property that any locally one-to-one reflexive open mapping of X into a Hausdorff space is globally one-to-one. Several problems are posed and some examples are given.

Keywords

Hausdorff spaceslocally connected and locally compact metric spacesgeneralized graphreflexive open mappingsone-to-one mappings

MSC classification

Secondary: 54C10: Special maps on topological spaces (open, closed, perfect, etc.) 54F50: Spaces of dimension $leq 1$; curves, dendrites 54F65: Topological characterizations of particular spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 3 , December 1989 , pp. 343 - 349
Copyright
Copyright © Australian Mathematical Society 1989

References

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