id: 05677405
dt: j
an: 05677405
au: Biasi, Carlos; de Mattos, Denise; dos Santos, Edivaldo L.
ti: Applications of the non-standard version of the Borsuk-Ulam theorem.
so: JP J. Geom. Topol. 9, No. 3, 273-284 (2009).
py: 2009
pu: Pushpa Publishing House, Allahabad, Uttar Pradesh, India
la: EN
cc:
ut: Borsuk-Ulam theorem; free maps; coincidence points; graphs
ci:
li: http://pphmj.com/abstract/4600.htm
ab: The authors intend to apply the nontandard version of the Borsuk-Ulam
theorem to graphs and the suspension $SX$ of a topologial space $X$. In
doing so, they establish some efficient methods. Surjectiveness of the
map $\text{Id}_*-ϕ^1_x$ is verified. A connected graph $X$ is
constructed with $φ:X\to X$ such that the determinant of $I-[φ^1_H]$
is not zero. Finally a physical interpretation of the nonstandard
version of the Borsuk-Ulam theorem is given.
rv: K. Chandrasekhara Rao (Kumbakonam)