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Abstrakty
We define a continuum of type lambda that admits a fixed-point-free map and has the condition that each of its layers has the fixed-point property. This answers a question of G. R. Gordh.
Wydawca
Rocznik
Tom
Strony
121--127
Opis fizyczny
Bibliogr. 16 poz., rys.
Twórcy
autor
- Department of Mathematics, California State University, Sacramento, Sacramento, California 95819-6051, USA
Bibliografia
- [1] R. H. Bing, Snake-like continua, Duke Math. J., 18 (1951) 653-663.
- [2] R. H. Bing, The elusive fixed point property, Amer. Math. Monthly, 76 (1969) 119-132.
- [3] G. R. Gordh, Jr., Monotone decompositions of irreducible Hausdorff continua, Ph.D. Dissertation, University of California, Riverside 1971.
- [4] G. R. Gordh, Jr., Monotone decompositions of irreducible Hausdorff continua, Pacific J. Math., 36 (1971) 647-658.
- [5] J. B. Fugate, A characterization of chainable continua, Canad. J. Math., 21 (1969) 383-393.
- [6] C. L. Hagopian, Uniquely arcwise connected plane continua have the fixed-point property, Trans. Amer. Math. Soc., 248 (1979) 85-104.
- [7] C. L. Hagopian, R. Mańka, Simple spirals on double Warsaw circles, Topology Appl., 128 (2003) 93-101.
- [8] O. H. Hamilton, A fixed point theorem for pseudo-arcs and certain other metric continua, Proc. Amer. Math. Soc., 2 (1951) 173-174.
- [9] K. Kuratowski, Théorie des continus irréductibles entre deux points II, Fund. Math., 10 (1927) 225-276.
- [10] K. Kuratowski, Topology, Vol. 2, 3rd ed., Monografie Mat., Tom 21, PWN, Warsaw 1961; English transl.: Academic Press, New York; PWN, Warsaw 1968.
- [11] I. W. Lewis, Continuum theory problems, Topology Proc., 8 (1983) 361-394.
- [12] R. Mańka, On spirals and the fixed point property, Fund. Math., 144 (1994) 1-9.
- [13] L. Mohler, A characterization of hereditarily decomposable snake-like continua, Colloq. Math., 28 (1973) 51-56.
- [14] R. L. Moore, Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc., 27 (1925) 416-428.
- [15] E. S. Thomas, Jr., Monotone decompositions of irreducible continua, Rozprawy Mat., 50 (1966) 1-74.
- [16] G. T. Whyburn, Analytic topology, Amer. Math. Soc. Colloq. Publ., 28 (1963).
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Bibliografia
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bwmeta1.element.baztech-article-BAT5-0001-0053