Maps which preserve graphs

Van C. Nall
1987 Proceedings of the American Mathematical Society  
In 1976 Eberhart, Fúgate, 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
more » ... so, some continua in addition to graphs are shown to be the images of partially confluent maps only.
doi:10.1090/s0002-9939-1987-0908670-x fatcat:gbbxxy35gra4toj72dklbx4lpq