Journal of the Ramanujan Mathematical Society

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Index of a Finitistic Space and a Generalization of the Topological Central Point Theorem


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1 NASI Senior Scientist, Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India
     

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In this paper we prove that if G is a p-torus (resp. torus) group acting without fixed points on a finitistic space X (resp. with finitely many orbit types), then the G-index iG(X) < ∞. Using this G-index we obtain a generalization of the Central Point Theorem and also of the Tverberg Theorem for any d-dimensional Hausdorff space.
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  • Index of a Finitistic Space and a Generalization of the Topological Central Point Theorem

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Authors

Satya Deo
NASI Senior Scientist, Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India

Abstract


In this paper we prove that if G is a p-torus (resp. torus) group acting without fixed points on a finitistic space X (resp. with finitely many orbit types), then the G-index iG(X) < ∞. Using this G-index we obtain a generalization of the Central Point Theorem and also of the Tverberg Theorem for any d-dimensional Hausdorff space.