Lusternik-Schnirelmann type invariants for Menger manifolds

Abstract

We study the $n$-dimensional category $ca{t}_n\left(X\right)$ of a compact space $X$, a counterpart to Lusternik-Schnirelmann category in the context of $n$-homotopy theory, and prove Menger manifold analogues of results due to Montejano and Wong for Hilbert cube manifolds.