A generalization of product inequality for the higher topological complexity

Abstract

In [4] M. Farber defined the topological complexity T C(X) of a path-connected space X. Generalizing this notion, ten years later, Yu. Rudyak introduced a sequence of invariants, called the higher topological complexities T Cn(X), for any path-connected space X in [7]. These invariants have their origin in the notion of the Schwarz genus of a fibration defined in [8]. One of the tools used to calculate these invariants is the product inequality for the Schwarz genus. In this paper, we will give a generalization of the product inequality of the higher topological complexity.