ON HIGHER TOPOLOGICAL COMPLEXITY OF PRODUCT OF TOPOLOGICAL SPACES

Abstract

The higher order topological complexity is Y.B. Rudyak introduced in 2010, this is a top ological invariant that has many relations with other invariants. To compute higher order topological complexity we usually have to introduce upper bounds by inequalities or by constructing section over the space and lower bound using the congruence property of topological space. In this paper, by using the inequalities for the upper bound of the product space and the property of the homogeneity of the product space, we give the results of the calculation of the product of topological spaces which have large topological complexity. These are important topological spaces in robot theory.