Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-28T11:44:02.102Z Has data issue: false hasContentIssue false
  • English
  • Français

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 tchewanS7N0W0, e-mail: bula@snoopy.usask.ca
E. D. Tymchatyn
Affiliation:
Department of Mathematics, University of Saskatchewan, Saskatoon, SaskatchewaS7N0W0, e-mail: tymchatyn@snoopyusask.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

1. Buskirk, R. D., Nikiel, J. and Tymchatyn, E. D., Totally regular curves as inverse limits, Houston J. Math. 18(1992),319–327.Google Scholar
2. Engelking, R., General Topology, Berlin, Heldermann Verlag, 1989.Google Scholar
3. Harrold, O. G. Jr., A note on strongly irreducible maps of an interval, Duke Math. J. 6(1940), 750–752.Google Scholar
4. Harrold, O. G., The role of local separating points in certain problems of continuum structure. In: Lectures in Topology, Univ. of Michigan Conf. 1940, 237-253, Ann Arbor, Univ. of Michigan Press, 1941.Google Scholar
5. Harrold, O. G., A mapping characterization ofPeano spaces, Bull. Amer. Math. Soc. 48(1942), 561–566.Google Scholar
6. Iliadis, S. D., Universal continuum for the class of completely regular continua, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 28(1980), 603–607.Google Scholar
7. Krasinkiewicz, J., On two theorems of Dyer, Colloq. Math. 50(1986), 201–208.Google Scholar
8. Kuratowski, K., Topology, vol. II, New York and Warsaw, Academic Press and PWN, Polish Scientific Publishers, 1968.Google Scholar
9. Nikiel, J., Images of arcs—a nonseparable version of the Hahn-Mazurkiewicz theorem, Fund. Math. 129 (1988), 91–120.Google Scholar
10. Nikiel, J., Locally connected curves viewed as inverse limits, Fund. Math. 133(1989), 125–134.Google Scholar
11. Nikiel, J.,Tuncali, H. M. and Tymchatyn, E. D., Continuous images of arcs and inverse limit methods, Mem. Amer. Math. Soc. (498) 104, 1993.Google Scholar
12. Treybig, L. B. and Ward, L. E. Jr., The Hahn-Mazurkiewicz problem. In: Topology and Order Structures I, Math. Centre Tracts 142, Amsterdam, 1981, 95–105.Google Scholar
13. Tymchatyn, E. D., Weakly confluent mappings and a classification of continua, Colloq. Math. 36(1976), 229–233.Google Scholar
14. Ward, L. E. Jr., An irreducible Hahn-Mazurkiewicz theorem, Houston J. Math. 3(1977), 285–290.Google Scholar
15. Whyburn, G. T., Analytic Topology, Providence, Rhode Island, Amer. Math. Soc. 1942.Google Scholar