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Cartesian factorization

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(in topology)

A factorization of a space into a topological product. An important problem on non-trivial Cartesian factorizations concerns the cubes and the Euclidean spaces . For instance, if a space is obtained from , , by identifying the points of an arc for which (cf. Wild imbedding), then and . Any smooth compact contractible manifold is a factor of an , . Any factor of , , is an , .

References

[1] Itogi Nauk. Algebra. Topol. Geom. 1965 (1967) pp. 227; 243


Comments

Another famous example is Bing's "Dog Bone" decomposition of -dimensional Euclidean space, its product with a line is homeomorphic to -dimensional Euclidean space.

References

[a1] R.H. Bing, "The cartesian product of a certain non-manifold and a line is ," Ann. of Math. , 70 (1959) pp. 399–412
[a2] R.J. Daverman, "Decompositions of manifolds" , Acad. Press (1986)
How to Cite This Entry:
Cartesian factorization. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cartesian_factorization&oldid=32893
This article was adapted from an original article by A.V. Chernavskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article