Geodesic
Size levels for arcs
Sam B. Nadler, Jr.1 ; Thelma West2
1 Department of Mathematics West Virginia University Morgantown, West Virginia 26505 U.S.A.
2 Department of Mathematics University of Southwestern Louisiana Lafayette, Louisiana 70504 U.S.A.
Fundamenta Mathematicae, Tome 141 (1992) no. 3, pp. 243-255 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm-141-3-243-255
Keywords: hyperspace, cyclic elements, absolute retract

Sam B. Nadler, Jr. 1 ; Thelma West 2

1 Department of Mathematics West Virginia University Morgantown, West Virginia 26505 U.S.A.
2 Department of Mathematics University of Southwestern Louisiana Lafayette, Louisiana 70504 U.S.A. 
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Sam B.  Nadler, Jr.; Thelma West. Size levels for arcs. Fundamenta Mathematicae, Tome 141 (1992) no. 3, pp. 243-255. doi: 10.4064/fm-141-3-243-255

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