this paper extends the notion of ditopology to the case where openness and closedness are given in terms of {em a priori} unrelated drading functions. the resulting notion of graded ditopology is considered both in the setting of lattices and in that textures, the relation between the two approaches being discussed in detail. interrelations between graded ditopologies and ditopologies on textur...

Let $H$ be an acylindrically hyperbolic group without nontrivial finite normal subgroups. We show that any system $S$ of equations with constants from is equivalent to a single equation. also the algebraic set associated is, up conjugacy, projection splitted equation (such has form $w(x\_1,\ldots,x\_n)=h$, where $w\in F(X)$, $h\in H$). From this we deduce following statement: $G$ arbitrary over...

Given a local Cohen-Macaulay ring (R,m), we study the interplay between the integral closedness – or even the normality – of an m-primary R-ideal I and conditions on the Hilbert coefficients of I . We relate these properties to the depth of the associated graded ring of I .

We give an answer to an open problem regarding the full enlargeability of a maximal monotone operator S : X ⇒ X∗ by Sse, the smallest enlargement belonging to a certain class of enlargements associated to S. Moreover, we prove the weak∗ closedness of the set ShS (ε1, x)+ThT (ε2, x) under a weak generalized interior regularity condition.

In this work, we introduce definitions of smooth strong compactness and smooth P-closedness for arbitrary L-fuzzy sets in smooth Lfuzzy topological spaces and study some of their properties. We also investigate relations between these concepts and the other definitions of compactness in smooth L-fuzzy spaces. Mathematics Subject Clasification: 54A40

In this paper, we consider the structure of maximally monotone operators in Banach space whose domains have nonempty interior and we present new and explicit structure formulas for such operators. Along the way, we provide new proofs of norm-to-weak∗ closedness and of property (Q) for these operators (as recently proven by Voisei). Various applications and limiting examples are given.

We introduce certain ideals of real-valued functions as a natural generalization of filters. We show that these ideals establish a canonical framework for the quantification of topological concepts, such as closedness, adherence, and compactness, in the setting of approach spaces. 2000 Mathematics Subject Classification. 54A05, 54D30.

In concurrency theory, there are several examples where the interleaved model of concurrency can distinguish between execution sequences which are not signiicantly diierent. One such example is sequences that diier from each other by stuttering, i. e., the number of times a state can adjacently repeat. Another example is executions that diier only by the ordering of independently executed event...