We consider constant mean curvature surfaces with finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces with three ends and genus zero were constructed and completely classified by the authors [GKS2, GKS1]. Here we extend the arguments to the case of an arbitrary number of ends, under the assumption that the asymptotic axes of the ends lie in a common plane...

In digital topology, it is well-known that, in 2D and in 3D, a digital set X ⊆ Z is digitally well-composed (DWC), i.e., does not contain any critical configuration, if its immersion in the Khalimsky grids H is well-composed in the sense of Alexandrov (AWC), i.e., its boundary is a disjoint union of discrete (n− 1)-surfaces. We show that this is still true in n-D, n ≥ 2, which is of prime impor...

The simplest bimodal combination of unimodal logics L1 and L2 is their fusion, L1 ⊗ L2, axiomatized by the theorems of L1 for 1 and of L2 for 2, and the rules of modus ponens, substitution and necessitation for 1 and for 2. Shehtman introduced the frame product L1 × L2, as the logic of the products of certain Kripke frames: these logics are two-dimensional as well as bimodal. Van Benthem, Bezha...

in this paper, a pointwise pseudo-metric function on the l-realline is constructed. it is proved that the topology induced by this pointwisepseudo-metric is the usual topology.

In this paper, a pointwise pseudo-metric function on the L-realline is constructed. It is proved that the topology induced by this pointwisepseudo-metric is the usual topology.

the concept of an $l$-bornology is introduced and the theory of $l$-bornological spacesis being developed. in particular the lattice of all $l$-bornologies on a given set is studied and basic properties ofthe category of $l$-bornological spaces and bounded mappings are investigated.

in this paper, the definition of meet-continuity on $l$-directedcomplete posets (for short, $l$-dcpos) is introduced. as ageneralization of meet-continuity on crisp dcpos, meet-continuity on$l$-dcpos, based on the generalized scott topology, ischaracterized. in particular, it is shown that every continuous$l$-dcpo is meet-continuous and $l$-continuous retracts ofmeet-continuous $l$-dcpos are al...