Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Universal maps on trees


Authors: Carl Eberhart and J. B. Fugate
Journal: Trans. Amer. Math. Soc. 350 (1998), 4235-4251
MSC (1991): Primary 54H25; Secondary 54F20
DOI: https://doi.org/10.1090/S0002-9947-98-02026-1
MathSciNet review: 1443871
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A map $f:R \to S$ of continua $R$ and $S$ is called a universal map from $R$ to $S$ if for any map $g:R \to S$, $f(x) = g(x)$ for some point $x \in R$. When $R$ and $S$ are trees, we characterize universal maps by reducing to the case of light minimal universal maps. The characterization uses the notions of combinatorial map and folded subedge of $R$.


References [Enhancements On Off] (What's this?)

  • 1. C. A. Eberhart, J. B. Fugate, and G. R. Gordh, Branchpoint Covering Theorems for Confluent and Weakly Confluent Maps, Proc. A.M.S, 55 (1976), 409-415. MR 53:14450
  • 2. W. Holsztynski, Universal Mappings and Fixed Point Theorems, Bull. Acad. Polon. Sci., XV (1967), 433-438. MR 36:4545
  • 3. W. Holsztynski, Universality of the product mappings onto products of $I^n$ and snake-like spaces, Fund. Math. 64 (1969), 147-155. MR 39:6249
  • 4. O.W. Lokuciewski, On a theorem on fixed points, Uspehi Mat. Nauk XII 3(75) 1957, 171-172.
  • 5. M. M. Marsh, Fixed Point Theorems for Certain Tree-like Continua, Dissertation, University of Houston, (1981).
  • 6. M. M. Marsh, u-mappings on trees, Pacific Journal of Mathematics, Vol. 127, No. 2 (1987), 373-387. MR 88f:54067
  • 7. S. B. Nadler, Jr., Universal Mappings and Weakly Confluent Mappings, Fund. Math, 110, (1980), 221-235. MR 82h:54057
  • 8. G. T. Whyburn, Analytic Topology, A.M.S. Colloq. Pub. XXVIII, (1963). MR 32:425

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 54H25, 54F20

Retrieve articles in all journals with MSC (1991): 54H25, 54F20


Additional Information

Carl Eberhart
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: carl@ms.uky.edu

J. B. Fugate
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: fugate@ms.uky.edu

DOI: https://doi.org/10.1090/S0002-9947-98-02026-1
Keywords: Minimal universal, combinatorial, tree, fixed point property
Received by editor(s): May 5, 1987
Received by editor(s) in revised form: January 21, 1997
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society