On lifting properties for confluent mappings

Charatonik, Janusz; Prajs, Janusz

doi:10.1090/S0002-9939-04-07537-9

On lifting properties for confluent mappings
HTML articles powered by AMS MathViewer

by Janusz J. Charatonik and Janusz R. Prajs PDF

Proc. Amer. Math. Soc. 133 (2005), 577-585 Request permission

Abstract:

Known results about lifting of paths for covering, light open and light confluent mappings are in some sense extended for all confluent mappings with the domain being a continuum having the arc property of Kelley. As an application we prove that each confluently tree-like continuum has the fixed point property.

References

R. H. Bing and F. B. Jones, Another homogeneous plane continuum, Trans. Amer. Math. Soc. 90 (1959), 171–192. MR 100823, DOI 10.1090/S0002-9947-1959-0100823-3
Janusz J. Charatonik, Włodzimierz J. Charatonik, and PawełKrupski, Dendrites and light open mappings, Proc. Amer. Math. Soc. 128 (2000), no. 6, 1839–1843. MR 1751997, DOI 10.1090/S0002-9939-00-05693-8
J. J. Charatonik, W. J. Charatonik and J. R. Prajs, Hereditarily unicoherent continua and their absolute retracts, Rocky Mountain J. Math. 34 (2004), no. 1, 83–110.
J. J. Charatonik, W. J. Charatonik and J. R. Prajs, Arc property of Kelley and absolute retracts for hereditarily unicoherent continua. Colloq. Math. 97 (2003), no. 1, 49–65.
J. J. Charatonik, W. J. Charatonik and J. R. Prajs, Confluent mappings and the arc property of Kelley, preprint.
J. J. Charatonik and P. Krupski, Dendrites and light mappings, Proc. Amer. Math. Soc. 132 (2004), 1211–1217.
J. J. Charatonik and J. R. Prajs, AANR spaces and absolute retracts for tree-like continua, Czechosl. Math. J. (to appear).
Morgan Ward and R. P. Dilworth, The lattice theory of ova, Ann. of Math. (2) 40 (1939), 600–608. MR 11, DOI 10.2307/1968944
A. Granas, Fixed point theorems for the approximative $\textrm {ANR}$-s, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1967), 15–19 (English, with Russian summary). MR 227917
Charles L. Hagopian, Fixed-point problems in continuum theory, Continuum theory and dynamical systems (Arcata, CA, 1989) Contemp. Math., vol. 117, Amer. Math. Soc., Providence, RI, 1991, pp. 79–86. MR 1112805, DOI 10.1090/conm/117/1112805
Sergio Sispanov, Generalización del teorema de Laguerre, Bol. Mat. 12 (1939), 113–117 (Spanish). MR 3
Józef Krasinkiewicz, Path-lifting property for 0-dimensional confluent mappings, Bull. Polish Acad. Sci. Math. 48 (2000), no. 4, 357–367. MR 1797901
T. Maćkowiak, Continuous mappings on continua, Dissertationes Math. (Rozprawy Mat.) 158 (1979), 95. MR 522934
Tadeusz Maćkowiak, Retracts of hereditarily unicoherent continua, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), no. 3-4, 177–183 (1981) (English, with Russian summary). MR 620356
T. Maćkowiak and E. D. Tymchatyn, Some classes of locally connected continua, Colloq. Math. 52 (1987), no. 1, 39–52. MR 891496, DOI 10.4064/cm-52-1-39-52
J. Mioduszewski, On continuous selections of multi-valued functions on dendrites, Prace Mat. 5 (1961), 73–77 (Polish, with Russian and English summaries). MR 0130674
Sam B. Nadler Jr., Continuum theory, Monographs and Textbooks in Pure and Applied Mathematics, vol. 158, Marcel Dekker, Inc., New York, 1992. An introduction. MR 1192552
Janusz R. Prajs, Continuous decompositions of Peano plane continua into pseudo-arcs, Fund. Math. 158 (1998), no. 1, 23–40. MR 1641220
Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
J. J. Corliss, Upper limits to the real roots of a real algebraic equation, Amer. Math. Monthly 46 (1939), 334–338. MR 4, DOI 10.1080/00029890.1939.11998880