3 problems

Compactness conjecture. Every Nyikos inverse topological semigroup is compact.

Let $G$ be the dual graph of an equivalence relation with countably many equivalence classes, each of countable size. For a closed subsemigroup $S$ of a full transformation monoid,…

Let $I(X)$ be the symmetric inverse semigroup on $X$, equipped with the topology under consideration, and let … be its multiplication map. Openness conjecture. The map $\circ$ is o…