Geodesic
A Map of a Polyhedron onto a Disk
Canadian mathematical bulletin, Tome 19 (1976) no. 4, pp. 483-485

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A map f: X → Y is said to be universal if for every map g:X → Y there exists an x ∈ X such that f(x) = g(x). In [2] W. Holsztynski observed that if B is a Boltyanskiĭ continuum (see [1]), then there exists a universal map f:B→ I 2 such that the product map fxf:BxB→I 2×I 2 is not universal. Using this he showed that B can be replaced by a two-dimensional polyhedron. He did not, however, give a concrete example. We exhibit explicitly a two-dimensional polyhedron K and a universal map f:K→ I 2 such that f×f:K×K→ I 2×I 2 is not universal. 
Strube, Richard F. E. A Map of a Polyhedron onto a Disk. Canadian mathematical bulletin, Tome 19 (1976) no. 4, pp. 483-485. doi: 10.4153/CMB-1976-072-3
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     title = {A {Map} of a {Polyhedron} onto a {Disk}},
     journal = {Canadian mathematical bulletin},
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     year = {1976},
     volume = {19},
     number = {4},
     doi = {10.4153/CMB-1976-072-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-072-3/}
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