Size levels for arcs

Fundamenta Mathematicae (1992)

• Volume: 141, Issue: 3, page 243-255
• ISSN: 0016-2736

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Abstract

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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.

How to cite

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Nadler, Sam, and West, T.. "Size levels for arcs." Fundamenta Mathematicae 141.3 (1992): 243-255. <http://eudml.org/doc/211963>.

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.},
author = {Nadler, Sam, West, T.},
journal = {Fundamenta Mathematicae},
keywords = {hyperspace; cyclic elements; absolute retract; Whitney map; arc; cyclic element; size level},
language = {eng},
number = {3},
pages = {243-255},
title = {Size levels for arcs},
url = {http://eudml.org/doc/211963},
volume = {141},
year = {1992},
}

TY - JOUR
AU - West, T.
TI - Size levels for arcs
JO - Fundamenta Mathematicae
PY - 1992
VL - 141
IS - 3
SP - 243
EP - 255
AB - 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.
LA - eng
KW - hyperspace; cyclic elements; absolute retract; Whitney map; arc; cyclic element; size level
UR - http://eudml.org/doc/211963
ER -

References

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1. [EN] C. Eberhart and S. B. Nadler, Jr., The dimension of certain hyperspaces, Bull. Acad. Polon. Sci. 19 (1971), 1071-1034. Zbl0235.54037
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. Zbl0405.54006
6. [W] G. Whyburn, Analytic Topology, Amer. Math. Soc. Colloq. Publ. 28, Amer. Math. Soc., Providence, R.I., 1949. Zbl0117.15804

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