Categorically closed countable semigroups

Categorically Closed Topological Groups

Let ~ C be a category whose objects are semigroups with topology and morphisms are closed semigroup relations, in particular, continuous homomorphisms. An object X of the category ~ C is called ~ C-closed if for each morphism Φ ⊂ X×Y in the category ~ C the image Φ(X) = {y ∈ Y : ∃x ∈ X (x, y) ∈ Φ} is closed in Y. In the paper we survey existing and new results on topological groups, which are ~...

On Countable Completions of Quotient Ordered Semigroups

A poset is said to be ω-chain complete if every countable chain in it has a least upper bound. It is known that every partially ordered set has a natural ω-completion. In this paper we study the ω-completion of partially ordered semigroups, and the topological action of such a semigroup on its ω-completion. We show that, for partially ordered semigroups, ω-completion and quotient with respect t...

The countable existentially closed pseudocomplemented semilattice

Remarks on Star Countable Discrete Closed Spaces

In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) Assuming 20 = 21 , there exists a normal absolutely star countable discrete clos...

SProc Categorically

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...