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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Maps which preserve graphs


Author: Van C. Nall
Journal: Proc. Amer. Math. Soc. 101 (1987), 563-570
MSC: Primary 54C10; Secondary 54F20, 54F50
DOI: https://doi.org/10.1090/S0002-9939-1987-0908670-X
MathSciNet review: 908670
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Abstract: In 1976 Eberhart, Fugate, and Gordh proved that the weakly confluent image of a graph is a graph. A much weaker condition on the map is introduced called partial confluence, and it is shown that the image of a graph is a graph if and only if the map is partially confluent.

In addition, it is shown that certain properties of one-dimensional continua are preserved by partially confluent maps, generalizing theorems of Cook and Lelek, Tymchatyn and Lelek, and Grace and Vought. Also, some continua in addition to graphs are shown to be the images of partially confluent maps only.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0908670-X
Keywords: Continuum, weakly confluent, partially confluent, suslinean, graph
Article copyright: © Copyright 1987 American Mathematical Society