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ArticleOriginal scientific text

Title

Size levels for arcs

Authors 1, 2

Affiliations

  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.

Abstract

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.

Keywords

ENG
hyperspace, cyclic elements, absolute retract

Bibliography

  1. [EN] C. Eberhart and S. B. Nadler, Jr., The dimension of certain hyperspaces, Bull. Acad. Polon. Sci. 19 (1971), 1071-1034.
  2. [K] K. Kuratowski, Topology, Vol. II, Academic Press, New York 1966.
  3. [N1] S. B. Nadler, Jr.. Hyperspaces of Sets, Marcel Dekker, New York 1978.
  4. [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.
  5. [P] A. Petrus, Contractibility of Whitney continua in C(X), General Topology Appl. 9 (1978), 275-288.
  6. [W] G. Whyburn, Analytic Topology, Amer. Math. Soc. Colloq. Publ. 28, Amer. Math. Soc., Providence, R.I., 1949.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm141/fm14134.pdf

Fundamenta Mathematicae
1992/141/3
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Pages:
243-255
Main language of publication
English
Received
1991-09-30
Published
1992
Exact and natural sciences