A result about a selection problem of Michael

Jordan, Francis; Nadler, Sam, Jr.

doi:10.1090/S0002-9939-00-05598-2

A result about a selection problem of Michael
HTML articles powered by AMS MathViewer

by Francis Jordan and Sam B. Nadler Jr. PDF

Proc. Amer. Math. Soc. 129 (2001), 1219-1228 Request permission

Abstract:

It is shown that a continuum that is an $S_4$ space in the sense of Michael must be hereditarily decomposable. This improves known results, thereby providing more evidence that such continua must be dendrites.

References

Richard G. Gibson and Tomasz Natkaniec, Darboux like functions, Real Anal. Exchange 22 (1996/97), no. 2, 492–533. MR 1460971, DOI 10.2307/44153937
Melvin R. Hagan, Equivalence of connectivity maps and peripherally continuous transformations, Proc. Amer. Math. Soc. 17 (1966), 175–177. MR 195063, DOI 10.1090/S0002-9939-1966-0195063-5
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. M. Jastrzębski, J. M. Jędrzejewski, and T. Natkaniec, On some subclasses of Darboux functions, Fund. Math. 138 (1991), no. 3, 165–173. MR 1121603, DOI 10.4064/fm-138-3-165-173
K. Kuratowski, Topology. Vol. II, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1968. New edition, revised and augmented; Translated from the French by A. Kirkor. MR 0259835
C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
Sam B. Nadler Jr., Hyperspaces of sets, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 49, Marcel Dekker, Inc., New York-Basel, 1978. A text with research questions. MR 0500811
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