Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-22T02:29:37.751Z Has data issue: false hasContentIssue false

Partial Orders on the 2-Cell

Published online by Cambridge University Press:  20 November 2018

E. D. Tymchatyn*
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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.

A partially ordered space is an ordered pair (X, ≤) where X is a compact metric space and ≤ is a partial ordering on X such that ≤ is a closed subset of the Cartesian product X×X. ≤ is said to be a closed partial order on X.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Tymchatyn, E. D., Antichains and products in partially ordered spaces, Trans. Amer. Math. Soc. 146 (1969) pp. 511-520.Google Scholar
2. Tymchatyn, E. D. The 2-cell as a partially ordered space, Pac. J. Math. 30 (1969) pp. 825-836.Google Scholar
3. Tymchatyn, E. D., Some order theoretic characterizations of the 3∼cell, Colloq. Math. 10 (1972) pp. 195-203.Google Scholar
4 Tymchatyn, E. D. and Ward, L.E. Jr., On three problems of Franklin and Wallace concerning partially ordered spaces, Coll. Math. 20 (1969) pp. 229-236.Google Scholar
5. Ward, L. E. Jr., Concerning Koch's Theorem on the existence of arcs, Pac. J. Math. 15 (1965) pp. 347-355.Google Scholar
6. Ward, L. E. Jr., Partially ordered topological spaces, Proc. Amer. Math. Soc. 5 (1954) pp. 144-161.Google Scholar
7. Ward, L. E. Jr., A note on dendrites and trees, Proc. Amer. Math. Soc. 5 (1954) pp. 992-994.Google Scholar
8. Wilder, R. L., Topology of Manifolds, Amer. Math. Soc., Providence, 1949.Google Scholar