Hostname: page-component-5b777bbd6c-sbgtn Total loading time: 0 Render date: 2025-06-22T04:45:42.485Z Has data issue: false hasContentIssue false
  • English
  • Français

Concerning Upper Semi-Continuous Decompositions of En Whose Non-Degenerate Elements are Polyhedral Arcs or Star-Like Continua

Published online by Cambridge University Press:  20 November 2018

L. B. Treybig
L. B. Treybig*
Affiliation:
The Tulane University of Louisiana, New Orleans, Louisiana
Rights & Permissions [Opens in a new window]

Extract

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.

In (1) Armentrout raised the question “Is there a monotone decomposition of E3 into arcs?” The analogous question for E2 was answered negatively by Roberts in (8). Our aim in this paper is to give a partial answer to Armentrout's question by proving the following theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1308 - 1314
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

The work on this paper was partially supported by XSF Grant Number GP-6220.

References

1. Armentrout, Steve, Monotone decompositions of E's, Annals of Math. Studies, No. 60, pp. 1–25 (Princeton Univ. Press, Princeton, N.J., 1966).Google Scholar
2. Bing, R. H., Partially continuous decompositions, Proc. Amer. Math. Soc. 6 (1955), 124–133.Google Scholar
3. Bing, R. H., Upper semi-continuous decompositions of E3, Ann. of Math. (2) 65 (1957), 363–374.Google Scholar
4. Bing, R. H., Pointlike decompositions of E3, Fund. Math. 50 (1962), 431–453.Google Scholar
5. Jones, Stephen L., The impossibility of filling En with arcs, Bull. Amer. Math. Soc. 74 (1968), 155–159.Google Scholar
6. McAuley, L. F., Some upper semi-continuous decompositions of E3 into E3, Ann. of Math. 2) 73 (1961), 437–457.Google Scholar
7. Moore, R. L., Foundations of point set theory, Amer. Math. Soc. Colloq. Publ., Vol. 13 (Amer. Math. Soc, Providence, R.I., 1932).Google Scholar
8. Roberts, J. H., Collections filling a plane, Duke Math. J. 2 (1936), 10–19.Google Scholar
9. Whyburn, G. T., Analytic topology, Amer. Math. Soc. Colloq. Publ., Vol. 32 (Amer. Math. Soc, Providence, R.I., 1949).Google Scholar