THE BORSUK-ULAM THEOREM IN A REAL CLOSED FIELD

Ikumitsu Nagasaki (Japan), Tomohiro Kawakami (Japan), Yasuhiro Hara (Japan) and Fumihiro Ushitaki (Japan)

Received January 19, 2009

Abstract

Let  be a cyclic group of order p. We prove the definable -version of the Borsuk-Ulam theorem in an o-minimal expansion    of a real closed field R.

Keywords and phrases: the Borsuk-Ulam theorem, o-minimal, real closed fields, finite groups, definable -maps.