• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.599-608
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• 1997

In this paper we give a generalization of the well-known Borsuk-Ulam theorem and its extensions to countably many products of spheres.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.891-901
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• 1998

We give a definition of the vector-valued index for Z-actions extending the numerical index in [9] and prove the extension theorem for Z-actions for showing basic properties of the vector-valued index.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.251-263
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• 2012

A CW complex B is said to be I-trivial if there does not exist a $\mathbb{Z}_2$-map from $S^{i-1}$ to S(${\alpha}$) for any vector bundle ${\alpha}$ over B a any integer i with i > dim ${\alpha}$. In this paper, we consider the question of determining whether $\Sigma^k\mathbb{R}P^n$ is I-trivial or not, and to this question we give complete answers when k $\neq$ 1, 3, 8 and partial answers when k = 1, 3, 8. A CW complex B is I-trivial if it is "W-trivial", that is, if for every vector bundle over B, all the Stiefel-Whitney classes vanish. We find, as a result, that $\Sigma^k\mathbb{R}P^n$ is a counterexample to the converse of th statement when k = 2, 4 or 8 and n $\geq$ 2k.