Size levels for arcs

Sam Nadler; T. West

Fundamenta Mathematicae (1992)

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

Abstract

top
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

top

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

@article{Nadler1992,
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 - Nadler, Sam
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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.