Compactness conjecture for Nyikos inverse topological semigroups

A Nyikos space is a locally compact, noncompact, countably compact space. An inverse topological semigroup is a topological semigroup in which every element has a unique inverse in the semigroup-theoretic sense.

Compactness conjecture. Every Nyikos inverse topological semigroup is compact.

This conjecture asks whether the inverse-semigroup structure forces compactness in the Nyikos setting. The paper's results establish compactness under additional hypotheses, but the general case remains open.