Size levels for arcs

Tom 141 / 1992

Sam B. Nadler, Jr., Thelma West Fundamenta Mathematicae 141 (1992), 243-255 DOI: 10.4064/fm_1992_141_3_1_243_255

Streszczenie

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.

Autorzy

  • Sam B. Nadler, Jr.Department of Mathematics
    West Virginia University
    Morgantown, West Virginia 26505
    U.S.A.
  • Thelma WestDepartment of Mathematics
    University of Southwestern Louisiana
    Lafayette, Louisiana 70504
    U.S.A.

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