JP Journal of Geometry and Topology
Volume 9, Issue 3, Pages 273 - 284
(November 2009)
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APPLICATIONS OF THE NON-STANDARD VERSION OF THE BORSUK-ULAM THEOREM
Carlos Biasi, Denise De Mattos and Edivaldo L. Dos Santos
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The non-standard version of the
Borsuk-Ulam theorem proved in [1], states that, under certain conditions on X
and j, for a given map
although the existence of a point
such that x
and
are collapsed by f
cannot always be assured, a very interesting phenomenon concerning the three
points
and
occurs when
for any
In this paper, we establish
efficient methods which allow to apply the non-standard version of the
Borsuk-Ulam theorem for graphs and for the suspension SX of a space X.
