Abstract In this paper, we establish a connection between categorical closedness and nontopologizability of semigroups. particular, for the class

We provide a systematic reconstruction of Abramsky's category SProc of synchronous processes Abr93]: SProc is isomorphic to a span category on a category of traces. The signiicance of the work is twofold: It shows that the original presentation of SProc in mixed formulations is unnecessary | a simple categorical description exists. Furthermore, the techniques employed in the reconstruction sugg...

Let $\mathcal C$ be a class of Hausdorff topological semigroups which contains all zero-dimensional semigroups. A semigroup $X$ is called C$-$closed$ if closed in each $Y\in \mathcal containing as discrete subsemigroup; $projectively$ for congruence $\approx$ on the quotient $X/_\approx$ C$-closed. $chain$-$finite$ any infinite set $I\subseteq X$ there are elements $x,y\in I$ such that $xy\noti...