On cat(X\(\backslash{} p\)) (Q1196601)

This paper discusses the relation between the Lyusternik-Shnirel'man category of \(X\) and of \(X\setminus p\), when \(X\) is a compact PL-manifold without boundary. The author proves that if \(\text{cat}(X)\geq 3\) (the category of a point is one), then \(\text{cat}(X\setminus p)\leq \text{cat}(X)\). Some examples are given to show that this is true in general for finite CW complexes.