Journal of the
Korean Mathematical Society JKMS

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

Keywords: vector-valued index, equivariant, rationally independent, Borsuk-Ulam theorem, extension theorem

MSC numbers: 58G10, 58D19, 11J72, 54C20