The set of balanced points with respect to 𝑆¹ and 𝑆³ actions of maps into Banach space

Mramor-Kosta, Neža

doi:10.1090/S0002-9939-1988-0929010-7

The set of balanced points with respect to $S^ 1$ and $S^ 3$ actions of maps into Banach space
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Proc. Amer. Math. Soc. 102 (1988), 723-727 Request permission

Abstract:

Let $G$ be the group of units in the field $F$, which is either $R$, $C$ or $H$, let $X$ be a free $G$-space, and let $f$ be a map from $X$ to a Banach space $E$ over $F$. In this paper we give an estimate for the size of the subset of $X$ consisting of points at which the average of $f$ is equal to zero. The result represents an extension of the Borsuk-Ulam-Yang theorem.

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Balanced orbits for fibre preserving maps of

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actions

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