Pacific Journal of Mathematics

$u$-mappings on trees.

M. M. Marsh

Article information

Source
Pacific J. Math., Volume 127, Number 2 (1987), 373-387.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102699568

Mathematical Reviews number (MathSciNet)
MR881765

Zentralblatt MATH identifier
0584.54030

Subjects
Primary: 54F20
Secondary: 54B25 54F50: Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03] 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20]

Citation

Marsh, M. M. $u$-mappings on trees. Pacific J. Math. 127 (1987), no. 2, 373--387. https://projecteuclid.org/euclid.pjm/1102699568


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References

  • [rop. 7] , it follows that / is universal. Suppose that X hasexactly m interior edges which arefolded by/. We assume that whenever /': Z -* Y is a w-mapping of a tree Z ontoY such that Z hasfewer than m interior edges which arefolded by/',then /' is universal. By way of contradiction, we assume that / is notuniversal. Let g: X -> Y bea mapping such that f(x) g(x) for each x e X.
  • [3,r2] ,r2] ,r2] ,r2] -* U,F] In a manner similar to that outlined in Example 2, it is easy to check that / has the desired properties. We also notice that a restriction of the mapping / would yield an example of a non-universal mapping which satisfies properties (1),(2),(3), and (5),but not (4). Let Xf = X - (39 b2]. Then the mapping f\x,: X' -> Y has the desired properties. Examples of non-universal mappings which do not satisfy property (1) or do not satisfy property (5) can also be given.
  • [1] D. Bellamy, A tree-like continuum without the fixed point property, Houston J. Math., 6 (1979), 1-14.
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