We show that the variety generated by the three-element Heyting algebra admits a meet dense, regular completion even though it is not closed under MacNeille completions.

The neighbourhood of a regular language of constant radius with respect to the prefix distance is always regular. We give upper bounds and matching lower bounds for the size of the minimal deterministic finite automaton (DFA) needed for the radius k prefix distance neighbourhood of an n state DFA that recognizes, respectively, a finite, a prefix-convex, a prefix-closed, a prefix-free, and a rig...

I investigate versions of the Maximality Principles for the classes of forcings which are <κ-closed, <κ-directed-closed, or of the form Col(κ,< λ). These principles come in many variants, depending on the parameters which are allowed. I shall write MPΓ(A) for the maximality principle for forcings in Γ, with parameters from A. The main results of this paper are: • The principles have many conseq...

A regular inductive limit of sequentially complete spaces is sequentially complete. For the converse of this theorem we have a weaker result: if indEn is sequentially complete inductive limit, and each constituent space En is closed in indEn, then indEn is α-regular.

We introduce the class of linearly S-closed spaces as a proper subclass H-closed spaces. This property lies between S-closedness and countable S-closedness. A space is called if only any semi-open chain cover posses member dense in space. It shown that extremally disconnected coincide. gave characterizations these terms s-accumulation points filter bases complete families open subsets. While re...

Any two triangulations of a closed surface with the same number of vertices can be transformed into each other by a sequence of flips, provided the number of vertices exceeds a number N depending on the surface. Examples show that in general N is bigger than the minimal number of vertices of a triangulation. The existence of N was known, but no estimate. This paper provides an estimate for N th...

Duplication is an operation generating a language from a single word by iterated application of rewriting rules u → uu on factors. We extend this operation to entire languages and investigate, whether the classes of the Chomsky hierarchy are closed under duplication. Here we treat mainly bounded duplication, where the factors duplicated cannot exceed a given length. While over two letters the r...

Let G be a non-connected reductive algebraic group over an algebraically closed field K and let D connected component of G. We investigate the Jordan classes we obtain description regular part closure class in terms induction G∘-orbits. use this result to show that Lusztig strata are locally closed.

Underlying the notion of an automatic structure is that of a synchronously regular (s-regular for short) set of pairs of strings. Accordingly we consider s-regular preex-rewriting systems showing that even for fairly restricted systems of this form connu-ence is undecidable in general. Then a close correspondence is established between the existence of an automatic structure that yields a preex...

Introduction. There has arisen in recent years a substantial body of work on “multiplier ideals” in commutative rings (see [La]). Multiplier ideals are integrally closed ideals with properties that lend themselves to highly interesting applications. One is tempted then to ask just how special multiplier ideals are among integrally closed ideals in general. In this note we show that in a two-dim...