A continuous injective map f from an open set U ⊂ Rⁿ to Rⁿ has open image f(U) and is a homeomorphism onto its image. Brouwer 1912. Immediate corollary (invariance of dimension): Rᵐ is not homeomorphic to Rⁿ for m ≠ n — dimension is a…
A continuous injective map f from an open set U ⊂ Rⁿ to Rⁿ has open image f(U) and is a homeomorphism onto its image. Brouwer 1912. Immediate corollary (invariance of dimension): Rᵐ is not homeomorphic to Rⁿ for m ≠ n — dimension is a…