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Embeddings of Topological Products of Circularly Chainable Continua

Published online by Cambridge University Press:  20 November 2018

L. Fearnley
L. Fearnley*
Affiliation:
Brigham Young University and University of Wisconsin
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In a recent paper (5), the author has established the Euclidean spaces of least dimension in which the topological products of finite collections of k-cell-like continua can be embedded. Specifically, it was shown that, for each pair of positive integers k and n, the topological product of any collection of nk-cell-like continua can be embedded in Euclidean space of dimension k(n + 1). This result includes a theorem of Bennett (1) that the topological product of any finite collection of n snakelike continua can be embedded in Euclidean space of dimension n + 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 715 - 723
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Bennett, R., Embedding products of chainable continua, Proc. Amer. Math. Soc., in press.Google Scholar
2. Bing, R. H., Embedding circle-like continua in the plane, Can. J. Math., 14 (1962), 113–128.Google Scholar
3. Eilenberg, S. and Steenrod, N., Foundations of algebraic topology (Princeton, 1952).Google Scholar
4. Fearnley, L., Characterization of the continuous images of the pseudo-arc, Trans. Amer. Math. Soc, 111 (1964), 380–399.Google Scholar
5. Fearnley, L., Embeddings of topological products of k-cell-like continua, Amer. J. Math., in press.Google Scholar
6. Kelley, J. L., General topology (New York, 1955).Google Scholar
7. Mardesic, S. and Segal, J., ∊-Mappings onto polyhedra, Trans. Amer. Math. Soc, 109 (1963), 146–163.Google Scholar
8. McCord, M., Inverse limit systems, Thesis, Yale University, 1963.Google Scholar
9. Whyburn, G. T., Analytic topology (Providence, 1942).Google Scholar