Generalized topological complexity and its monoidal version

Abstract

In the context of the Lusternik–Schnirelmann category, Srinivasan demonstrated that when the space under consideration is an absolute neighborhood retract, its category can be realized through arbitrary subsets, not necessarily open ones. The primary aim of this survey is to illustrate how this result has been extended to the case of topological complexity and its monoidal version, along with some of its most significant implications.