Whitney Preserving Maps onto Dendrites

• Autorzy: Matsuhashi, E.
• Języki publikacji: EN

Abstrakty

EN

We prove the following results. (i) Let X be a continuum such that X contains a dense arc component and let D be a dendrite with a closed set of branch points. If f:X→D is a Whitney preserving map, then f is a homeomorphism. (ii) For each dendrite D′ with a dense set of branch points there exist a continuum X′ containing a dense arc component and a Whitney preserving map f′:X′→D′ such that f′ is not a homeomorphism.

Słowa kluczowe

EN

Whitney preserving map; Whitney map; Whitney levels; hyperspaces

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: Vol. 60, no 2
• Strony: 155--163
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Matsuhashi, E.

• Department of Mathematics Faculty of Engineering Shimane University Matsue, Shimane 690-8504 Japan,

Bibliografia

• [1] J. J. Charatonik, W. J. Charatonik and J. R. Prajs, Mapping hierarchy for dendrites, Dissertationes Math. (Rozprawy Mat.) 333 (1994), 52 pp.
• [2] B. Espinoza Reyes, Whitney preserving functions, Topology Appl. 126 (2002), 351–358.
• [3] —, Whitney preserving maps onto decomposition spaces, Topology Proc. 29 (2005), 115–125.
• [4] B. Espinoza and A. Illanes, Whitney preserving maps on finite graphs, Topology Appl. 158 (2011), 1033–1044.
• [5] A. Illanes and S. B. Nadler Jr., Hyperspaces: Fundamentals and Recent Advances, Pure Appl. Math. Ser. 216, Dekker, New York, 1999.
• [6] K. Kuratowski, Topology, Vol. II, Academic Press, New York, 1968. Whitney Preserving Maps onto Dendrites 163
• [7] E. Matsuhashi, Some remarks on Whitney preserving maps, Houston J. Math. 36 (2010), 935–943
• [8] J. van Mill, The Infinite-Dimensional Topology of Function Spaces, North-Holland, Amsterdam, 2001.
• [9] S. B. Nadler Jr., Continuum Theory: An Introduction, Dekker, New York, 1992.
• [10] Y. Sternfeld, Mappings in dendrites and dimension, Houston J. Math. 19 (1993), 483–497.

Identyfikatory

DOI

10.4064/ba60-2-5