Embedding of the dunce hat (Q2839324)

The authors prove that the Borsuk contractible non-collapsible 2-polyhedron, commonly called the \(dunce\) \(hat\), does not embed in any product of two curves but quasi-embeds in the \textit{three-page book}. Their purpose is to show that for every positive integer \(n\) there exists a polyhedron \(X\) which quasi-embeds in the finite product of Menger curve \(\mu ^{n}\) but does not embed in \(\mu ^{n}\). They also ask for a possible characterization of the 2-dimensional polyhedra that are quasi-embeddable in a product of two curves.