Sur le plongement de 𝑋×𝐼ⁿ⁻² dans une 𝑛-variété

Cauty, Robert

doi:10.1090/S0002-9939-1985-0787904-7

Sur le plongement de $X\times I^ {n-2}$ dans une $n$-variété
HTML articles powered by AMS MathViewer

by Robert Cauty PDF

Proc. Amer. Math. Soc. 94 (1985), 516-522 Request permission

Abstract:

We prove that if $X$ is a locally connected continuum such that the product $X \times {I^{n - 2}}$ of $X$ and an $\left ( {n - 2} \right )$-cube can be embedded in an $n$-manifold, then $X$ is locally planar. An example shows that the converse is false.

References

K. Borsuk, On embedding curves in surfaces, Fund. Math. 59 (1966), 73–89. MR 200910, DOI 10.4064/fm-59-1-73-89

Compte-rendu de

6

26

Schieffelin Claytor, Peanian continua not imbeddable in a spherical surface, Ann. of Math. (2) 38 (1937), no. 3, 631–646. MR 1503359, DOI 10.2307/1968606
Witold Rosicki, On topological factors of $3$-dimensional locally connected continuum embeddable in $E^{3}$, Fund. Math. 99 (1978), no. 2, 141–154. MR 482692, DOI 10.4064/fm-99-2-141-154
T. Benny Rushing, Topological embeddings, Pure and Applied Mathematics, Vol. 52, Academic Press, New York-London, 1973. MR 0348752
Beauregard Stubblefield, Some imbedding and nonimbedding theorems for $n$-manifolds, Trans. Amer. Math. Soc. 103 (1962), 403–420. MR 143189, DOI 10.1090/S0002-9947-1962-0143189-5