  In the context of the Lusternik-Schnirelmann category, researcher T.
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.
