An elementary proof of invariance of domain and its consequences
Abstract
Let be a open subset of a Euclidean space R. Then, given any continuous injective mapping from to R, the image () is also open in R. The above is the statement of the invariance of domain theorem for Euclidean space; In this thesis, we present an elementary proof of the theorem that does not involve tools from algebraic topology and introduce an important consequence of the theorem: Euclidean spaces of different dimensions are not homeomorphic.
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Topology and Set Theory
Advanced Banach Space Theory
Publication details
- Journal / source
- Aaltodoc (Aalto University)
- Publication date
- 24 February 2026
- Language
- EN
- Document type
- Thesis