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

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