let s be a monoid and x a class of s-acts which is closed under coproducts. the object of this article is to find conditions under which all s-acts have x-precovering. we have shown that the existence of torsion-free precovering implies the existence of torsion-free covering. this work is an attempt to further facilitate the study of the conjecture that all s-acts have flat cover.

This paper is motivated by the open question whether the union of two disjoint NPcomplete sets always is NP-complete. We discover that such unions retain much of the complexity of their single components. More precisely, they are complete with respect to more general reducibilities. Moreover, we approach the main question in a more general way: We analyze the scope of the complexity of unions o...

A linearly ordered structure is weakly o-minimal if all of its definable sets in one variable are the union of finitely many convex sets in the structure. Weakly o-minimal structures were introduced by Dickmann, and they arise in several contexts. We here prove several fundamental results about weakly o-minimal structures. Foremost among these, we show that every weakly o-minimal ordered field ...

We use twisted sheaves and their moduli spaces to study the Brauer group of a scheme. In particular, we (1) show how twisted methods can be efficiently used to re-prove the basic facts about the Brauer group and cohomological Brauer group (including Gabber’s theorem that they coincide for a separated union of two affine schemes), (2) give a new proof of de Jong’s periodindex theorem for surface...

abstract   background: the tibial diaphyseal fractures are the most common type of long bone fractures encountered by most orthopedic surgeons. in accordance with descriptive indices of tibia fractures on the basis of their location in the bone, distal tibia fractures have the second incidence of all tibia fractures after the middle tibia fractures. the purpose of the study was to assess the co...

Families of Languages AFL thm if F is closed under substitution with λ-free regular sets, morphism, union with regular sets [easy for cfg] & intersection with regular sets, then F is closed under inverse morphism Figure 26: closure properties of CF II 12 intersection with regular languages a;A/α a a;A/α λ;A/α λ;A/α { } } { ⇒ ⇒ { anbn | n ≥ 1 }∗ ∩ { w ∈ {a, b}∗ |#ax even } r1 p1 q1 r0 p0 q0 r p ...

The term CW-complex comes from “closure-finite with the weak topology”, where “closure-finite” refers to A3 and “weak topology” refers to A4. A finite complex is a CW-complex with only finitely many cells. Observe that if X is a finite complex, A4 is redundant, since W is the union of the compact sets φα((φ n α) −1W ), and these are closed since X is Hausdorff. If X has cells of dimension n but...

The notion of a cell and that of a cell decomposition has been a central one in the study of certain first-order theories. A cell is a particular kind of definable set. The notion of a cell was first explicitly considered in [8], in the context of the theory of real closed fields. Collins defined a class of cells in this context, and showed that every definable subset of a real closed field is ...

We study, for the first time, maximum modulus set of a quasiregular map. It is easy to see that these sets are necessarily closed, and contain at least one point each modulus. Blumenthal showed entire maps either whole plane, or countable union analytic curves. show in case, by way contrast, any closed containing can be attained as These examples all polynomial type. also that, subject an addit...