Abstract
This work uses Nielsen coincidence theory to discuss solutions for the geometric Borsuk–Ulam question. It considers triples (X,τ;Y) where X and Y are topological spaces and τ is a free involution on X, (X,τ;Y) satisfies the Borsuk–Ulam theorem if for any continuous map f:X→Y there exists a point x∈X such that f(x)=f(τ(x)). Borsuk–Ulam coincidence classes are defined and a notion of essentiality is defined. The classical Borsuk–Ulam theorem and a version for maps between spheres are proved using this approach.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
