An exactly two-to-one map from an indecomposable chainable continuum

• Autorzy: Krzempek J.
• Języki publikacji: EN

Abstrakty

EN

It is shown that a certain indecomposable chainable continuum is the domain of an exactly two-to-one continuous map. This answers a question of Jo W. Heath.

Słowa kluczowe

EN

chainable continuum (= arclike continuum); indecomposable continuum; Knaster bucket handle continuum; exactly two-to-one map

PL

continuum nierozkładalne

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 3
• Strony: 335--339
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Krzempek J.

• Institute of Mathematics, Technical University of Silesia, Kaszubska 23, 44-100 Gliwice, Poland,

Bibliografia

• [1] A. V. Chernavskiĭ, The impossibility of a strictly double continuous partition of a homology cube, Dokl. Akad. Nauk SSSR 144 (1962), 286-289 (in Russian); English transl.: Soviet Math. Dokl. 3 (1962), 726-729.
• [2] W. Dębski, Two-to-one maps on solenoids and Knaster continua, Fund. Math. 141 (1992), 277-285.
• [3] P. Gilbert, n-to-one mappings of linear graphs, Duke Math. J. 9 (1942), 475-486.
• [4] O. G. Harrold, The non-existence of a certain type of continuous transformation, Duke Math. J. 5 (1939), 789-793.
• [5] J. W. Heath, Treelike continua and exactly k-to-one functions, Proc. Amer. Math. Soc. 105 (1989), 765-772.
• [6] -, 2-to-one maps with hereditarily indecomposable images, ibid. 113 (1991), 839-846.
• [7] -, 2-to-1 maps on hereditarily indecomposable continua, Trans. Amer. Math. Soc. 328 (1991), 433-444.
• [8] -, Four key questions in the theory of 2-to-1 maps, in: Topology. Theory and Applications, II, Colloq. Math. Soc. János Bolyai 55, North-Holland, Amsterdam, 1993, 301-305.
• [9] -, Exactly k-to-1 maps: from pathological functions with finitely many discontinuities to well-behaved covering maps, in: Continua. With the Houston Problem Book, Lecture Notes in Pure and Appl. Math. 170, Dekker, New York, 1995, 89-102.
• [10] J. Mioduszewski, On two-to-one continuous functions, Rozprawy Mat. (Dissertationes Math.) 24 (1961).
• [11] S. B. Nadler, Continuum Theory. An Introduction, Monogr. Textbooks Pure Appl. Math. 158, Dekker, New York, 1992.
• [12] I. Rosenholtz, Open maps of chainable continua, Proc. Amer. Math. Soc. 42 (1974), 258-264.