Serdica Mathematical Journal, Vol. 26, No 1, (2000), 1p-4p
Abstract:
An embedding X ⊂ G of a topological space X into a topological group G is called functorial if every homeomorphism of X extends
to a continuous group homomorphism of G. It is shown that the interval [0, 1] admits no functorial embedding into a finite-dimensional or metrizable
topological group.