Compactifications as closures of graphs

Graph Closures and Metric Compactifications of Tv

It is shown that all compactifications of the positive integers N which have metrizable remainders are themselves metrizable. This is done by first proving that each Hausdorff compactification of a noncompact locally compact space is the graph closure in an appropriate space. It is then shown that any two compactifications of N which have homeomorphic metrizable remainders are homeomorphic.

Intersection cohomology of B ×B-orbit closures in group compactifications

An adjoint semi-simple group G has a “wonderful” compactification X, which is a smooth projective variety, containing G as an open subvariety. X is acted upon by G×G and, B denoting a Borel subgroup of G, the group B × B has finitely many orbits in X. The main results of this paper concern the intersection cohomology of the closures of the B × B-orbits. Examples of such closures are the “large ...

Toric Ideals of Integral Closures from Graphs

A graph-theoretic method, simpler than existing ones, is used to characterize the minimal set of monomial generators for the integral closure of any polynomial ring generated by quadratic monomials. The toric ideal of relations between these generators is generated by a set of graphically described binomials. The spectra of the original ring and of its integral closure turn out to be canonicall...

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

Maintenance of Transitive Closures and Transitive Reductions of Graphs