Submetrizability in semitopological groups

Remarks on extremally disconnected semitopological groups

Answering recent question of A.V. Arhangel’skii we construct in ZFC an extremally disconnected semitopological group with continuous inverse having no open Abelian subgroups.

The Category of Semitopological S-Acts

Let S-Top be the category of topological S-acts over a topological semigroup S and S-SemiTop be the category of semitopological S-acts over a semitopological semigroup S. It is obvious that any topological S-act is a semitopological S-act, however we will see that the converse is not true in general. In this note, we study the universal objects in the category of semitopological S-acts and intr...

Semitopological Bl-algebras and Mv -algebras

In this paper, by considering the notion of upsets we construct some topologies on BLalgebras. We show that any BL-algebras with respect to these topologies formes semitopological BLalgebra. Then we obtain some of the topological aspects of theses structures such as connectivity and compactness. Moreover, we introduced two kinds of semitopological MV -algebra by using two kinds of definition of...

A cone theoretic Krein-Milman theorem in semitopological cones

In this paper, a Krein-Milman  type theorem in $T_0$ semitopological cone is proved,  in general. In fact, it is shown that in any locally convex $T_0$ semitopological cone, every convex compact saturated subset is the compact saturated convex hull of its extreme points, which improves the results of Larrecq.

Groups in Polygroups