Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-15T18:44:52.674Z Has data issue: false hasContentIssue false
  • English
  • Français

Arcs, Semigroups, and Hyperspaces

Published online by Cambridge University Press:  20 November 2018

M. M. McWaters
M. M. McWaters*
Affiliation:
University of South Florida, Tampa, Florida
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.

Several years ago Kelley (2) showed that if X is a metric continuum then S(X), the space of non-null, closed subsets of X, and C(X), the space of non-null, closed, connected subsets of X, with the Vietoris topology, are arcwise connected continua. He further showed that S(X) is acyclic. In this note we extend these results to non-metric continua.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1207 - 1210
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Hunter, R. P., Note on arcs in semigroups, Fund. Math. 49 (1961), 233–245.Google Scholar
2. Kelley, J. L., Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22–36.Google Scholar
3. Koch, R. J., Arcs in partially ordered spaces, Pacific J. Math. 9 (1959), 723–728.Google Scholar
4. Koch, R. J. and Wallace, A. D., Notes on inverse semigroups, Rev. Roumaine Math. Pures Appl. 9 (1964), 19–24.Google Scholar
5. Michael, E. A., Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152–182.Google Scholar
6. Wallace, A. D., Acyclicity of compact connected semigroups, Fund. Math. 50 (1961), 99–105.Google Scholar
7. Ward, L. E., Jr., Mobs, trees, and fixed points, Proc. Amer. Math. Soc. 8 (1957), 798–804.Google Scholar