Uniform versions of index for uniform spaces with free involutions

作者：Kaur Jaspreet^*

来源：Topology and Its Applications, 2013, 160(7): 896-905.

DOI：10.1016/j.topol.2013.03.002

• Uniform spaces with free involutions
• B-index (co-index)
• u-Equivariant function
• uB-index
• uBU-index

In this paper, uniform versions of index for uniform spaces equipped with free involutions are introduced and studied. They are mainly based on B-index defined and studied by C.-T. Yang in 1955, index studied by Conner and Floyd in 1960 and further development well collected by J. Matousek in his book on using the Borsuk-Ulam theorem in 2003. Interrelationships between these uniform versions of index are established. Examples of uniform spaces with finite B-index but infinite uniform version of index are given. It is shown that for a uniform space X with a free involution T, a dense T-invariant subspace is capable of determining the uniform version of index of (X, T). Connections between uniform versions of coloring and uniform versions of index is also indicated.

• 出版日期2013-4-15