Semigroup Closures of Finite Rank Symmetric Inverse Semigroups

We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse semigroup of finite transformations $\mathscr{I}_\lambda^n$ of the rank $\leqslant n$ is algebraically closed in the class of (semi)topological inverse semigroups with continuous inversion. We also derive related results about the nonexistence of (partial) compactifications of classes of semigroups that we consider.Comment: With the participation of the new coauthor - Jimmie Lawson - the manuscript has been substantially revised and expanded. Accordingly, we have also changed the manuscript titl

Use of SMS texts for facilitating access to online alcohol interventions: a feasibility study

A41 Use of SMS texts for facilitating access to online alcohol interventions: a feasibility study In: Addiction Science & Clinical Practice 2017, 12(Suppl 1): A4

Homomorphisms of nearrings of continuous functions from topological spaces into the asymmetric nearring

AbstractThere is a unique (up to isomorphism) topological nearring N, whose additive group is the two-dimensional Euclidean group, which has an identity but is not zero symmetric. For any topological space X, we denote by N(X) the nearring of all continuous functions from X to N where the operations on N(X) are the pointwise operations. We determine all the homomorphisms from the nearring N(X) into N(Y) when X is realcompact and Y is completely regular and Hausdorff. This result is then used to show that if both X and Y are either compact and Hausdorff or realcompact generated spaces then the endomorphism semigroups of N(X) and N(Y) are isomorphic if and only if the spaces X and Y are homeomorphic