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Far East Journal of Mathematical Sciences (FJMS)

Abstract:
Let k be a positive integer greater than 1 and

be the cyclic group of order k. Let X be an arcwise connected free

-space and Y be a Hausdorff free

-space. If there exists a positive integer n such that

for

and

then there is no continuous

-map from X to Y.

We also prove a definable version of this topological version in an o-minimal expansion of

of a real closed field R.

Keywords and phrases: Borsuk-Ulam theorem, finite groups, continuous

-maps, o-minimal, definable

-maps, real closed fields.

Number of Downloads: 358 | Number of Views: 1158

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P-ISSN: 0972-0871

E-ISSN: 2584-1246

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