Uniform versions of index for uniform spaces with free involutions (Q390798)

The classical Borsuk-Ulam theorem has been extended in various directions. \textit{C.-T. Yang} [Ann. Math. (2) 62, 271--283 (1955; Zbl 0067.15202)] associated a numerical invariant called the \(B\)-\(index\) to a compact Hausdorff space equipped with a free involution. Later \textit{P. E. Conner} and \textit{E. E. Floyd} [Bull. Am. Math. Soc. 66, 416--441 (1960; Zbl 0106.16301)] defined this invariant in a more general setting. In the paper under review, uniform versions of the index, uB-index and uBU-index, for uniform spaces equipped with free uniformly continuous involutions are introduced and investigated. The main result of the paper is the inequality B-index \(\leq\) uBU-index \(\leq\) uB-index.