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The Königsberg Bridge Problemfor Peano Continua

Published online by Cambridge University Press:  20 November 2018

W. Bula ,
J. Nikiel  and
E. D. Tymchatyn
W. Bula
Affiliation:
Department of Mathematics, University of Saskatchewan, Saskatoon, Saska tchewan S7N0W0, e-mail: bula@snoopy.usask.ca
E. D. Tymchatyn
Affiliation:
Department of Mathematics, University of Saskatchewan, Saskatoon, Saskatchewa S7N0W0, e-mail: tymchatyn@snoopyusask.ca
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Abstract

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Peano continua which are images of the unit interval [0,1] or the circle S under a continuous and irreducible map are investigated. Necessary conditions for a space to be the irreducible image of [0,1] are given, and it is conjectured that these conditions are sufficient as well. Also, various results on irreducible images of [0,1] and S are given within some classes of regular curves. Some of them involve inverse limits of inverse sequences of Euler graphs with monotone bonding maps.

Keywords

54E4005C4554F1554F5054C10Peano continuumEuler graphregular continuumtotally regular continuumcompletely regular continuumirreducible maplocal separating point

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 6 , 01 December 1994 , pp. 1175 - 1187
Copyright
Copyright © Canadian Mathematical Society 1994

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