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Universal maps on trees
Author(s):
Carl
Eberhart;
J.
B.
Fugate
Journal:
Trans. Amer. Math. Soc.
350
(1998),
4235-4251.
MSC (1991):
Primary 54H25;
Secondary 54F20
MathSciNet review:
1443871
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Abstract:
A map  of continua  and  is called a universal map from  to  if for any map  ,  for some point  . When  and  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  .
References:
- 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
 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
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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:
10.1090/S0002-9947-98-02026-1
PII:
S 0002-9947(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
Copyright of article:
Copyright
1998,
American Mathematical Society
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