Clifford and Preston (1961) showed several important characterizations of right groups. It was shown in Roy and So (1998) that, among topological semigroups, compact right simple or left cancellative semigroups are in fact right groups, and the closure of a right simple subsemigroup of a compact semigroup is always a right subgroup. In this paper, it is shown that such results can be generalize...

We revisit Ekedahl, Lando, Shapiro and Vainshtein’s compactification of the stack of Hurwitz covers. By drawing a connection with the Harris and Mumford stack of admissible covers we give a new geometric interpretation of boundary points of the ELSV compactification. As a byproduct we establish that this compactification holds for any algebraically closed field of sufficiently high characteristic.

We generalize the concept of near weight stated in [2007, IEEE Trans. Inform. Theory 53(5), 1919–1924] in the sense that we consider maps to arbitrary wellordered semigroups instead of the nonnegative integers. This concept can be used as a tool to study AG codes based on more than one point via elementary methods only.

We find here another (not of the CROC-type) compactification of the Kontsevich spaces K(m,n). This compactification is a Stasheff-type compactification, in particular, it is exactly the Stasheff compactification when n = 1 or m = 1. The boundary strata of this compactification are products of the spaces K(m, n) and of the Stasheff polyhedra. Then we construct a dg Lie algebra naturally associat...

In this paper we introduce the notion of fuzzy  semigroup via fuzzy partial ordering and investigate some properties connected with fuzzy  semigroup. Keyword: Fuzzy  semigroup

We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p, q). We prove that each topological semigroup S with pseudocompact square contains no dense copy of C(p, q). On the other hand, we construct a consistent example of a Tychonov countably compact semigroup containing a copy of C(p, q). In this paper we study the structural prope...

In the paper we study (countably) compact and (absolutely) H-closed primitive topological inverse semigroups. We describe the structure of compact and countably compact primitive topological inverse semigroups and show that any countably compact primitive topological inverse semigroup embeds into a compact primitive topological inverse semigroup. In this paper all spaces are Hausdorff. A semigr...

In 1969, P. Deligne and D. Mumford compactified the moduli space of curves Mg,n. Their compactification Mg,n is a projective algebraic variety, and as such, it has an underlying analytic structure. Alternatively, the quotient of the augmented Teichmüller space by the action of the mapping class group gives a compactification of Mg,n. We put an analytic structure on this quotient and prove that ...