The quasi Scott (Lawson) topology and q-continuous (q-algebraic) complete lattices

Lawson Topology in Continuous Lattices

Let S, T be semilattices. Let us assume that if S is upper-bounded, then T is upper-bounded. A map from S into T is said to be a semilattice morphism from S into T if: (Def. 1) For every finite subset X of S holds it preserves inf of X. Let S, T be semilattices. One can check that every map from S into T which is meet-preserving is also monotone. Let S be a semilattice and let T be an upper-bou...

Quasi-complete Q-groups Are Bounded

From the frontier of this paper, unless specified something else, let it be agreed that all groups into consideration are p-primary abelian for some arbitrary but fixed prime p written additively as is the custom when dealing with abelian group theory. The present short note is a contribution to a recent flurry of our results in [6]. Standardly, all notions and notations are essentially the sam...

Lawson Topology in Continuous Lattices1

Let S, T be semilattices. Let us assume that if S is upper-bounded, then T is upper-bounded. A map from S into T is said to be a semilattice morphism from S into T if: (Def. 1) For every finite subset X of S holds it preserves inf of X . Let S, T be semilattices. Observe that every map from S into T which is meet-preserving is also monotone. Let S be a semilattice and let T be an upper-bounded ...

ALGEBRAIC SURFACES WITH ' q

Complete arcs on the parabolic quadric Q(4, q)

Using the representation T2(O) of Q(4, q) and algebraic methods, we prove that complete (q2 − 1)-arcs of Q(4, q) do not exist when q = ph, p odd prime and h > 1. As a by-product we prove an embeddability theorem for the direction problem in AG(3, q). © 2007 Elsevier Inc. All rights reserved.