Size levels for arcs

• Autorzy: Sam B. Jr. Nadler , T. West
• Języki publikacji: EN

Abstrakty

EN

We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.

Słowa kluczowe

EN

hyperspace; cyclic elements; absolute retract

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1992
• Tom: 141
• Numer: 3
• Strony: 243-255

Daty

wydano

1992

otrzymano

1991-09-30

Twórcy

autor

Sam B. Jr. Nadler

• Department of Mathematics, West Virginia University, Morgantown, West Virginia 26505, U.S.A.

autor

T. West

• Department of Mathematics, University of Southwestern Louisiana, Lafayette, Louisiana 70504, U.S.A.

Bibliografia

• [EN] C. Eberhart and S. B. Nadler, Jr., The dimension of certain hyperspaces, Bull. Acad. Polon. Sci. 19 (1971), 1071-1034.
• [K] K. Kuratowski, Topology, Vol. II, Academic Press, New York 1966.
• [N1] S. B. Nadler, Jr.. Hyperspaces of Sets, Marcel Dekker, New York 1978.
• [N2] S. B. Nadler, Some problems concerning hyperspaces, in: Topology Conference (V.P.I. and S.U.), R. F. Dickman, Jr. and P. Fletcher (eds.), Lecture Notes in Math. 375, Springer, New York 1974, 190-197.
• [P] A. Petrus, Contractibility of Whitney continua in C(X), General Topology Appl. 9 (1978), 275-288.
• [W] G. Whyburn, Analytic Topology, Amer. Math. Soc. Colloq. Publ. 28, Amer. Math. Soc., Providence, R.I., 1949.