Lemma 1. There are ω1 disjoint stationary subsets of ω1. Proof. Let Cub(ω1) = {X ⊆ ω1 : ∃C ⊆ X(C is club on ω1)}. Then Cub(ω1) is countably complete filter. Its dual ideal Cub (ω1) = {X ⊆ ω1 : ∃X ′ ∈ Cub(ω1)(X = ω1\X ′)} is countably complete and contains all singletons and so all countable subsets of ω1. Recall also that X ⊆ ω1 is stationary if and only if X / ∈ Cub(ω1). For every ρ < ω1 let f...

We study localizing and colocalizing subcategories of a comodule category of a coalgebra C over a field, using the correspondence between localizing subcategories and equivalence classes of idempotent elements in the dual algebra C∗. In this framework, we give a useful description of the localization functor by means of the Morita–Takeuchi context defined by the quasi-finite injective cogenerat...

In this paper we provide sufficient conditions in order to show that the set image of a continuous and shift-commuting map defined on shift space over an arbitrary discrete alphabet is also space; additionally, if such injective, then its inverse shift-commuting.

The determination of the injective and projective members of a category is usually a challenging problem and adds to knowledge of the category. In this paper we consider these questions for the category of Heyting algebras. There has been a lack of uniformity in terminology in recent years. In [6] Heyting algebras are referred to as pseudo-Boolean algebras, and in [1] they are called Brouwerian...

In any concrete category C the natural problem of whether epimorphisms are surjective maps arise, as well as the dual problem of whether the monomorphisms are injective maps. This type of problems have already been studied before in several well known categories: for example in [6] it is shown that the property of epimorphisms of being surjective holds in the categories of von Neumann algebras,...

in this paper, we introduce the concept of rarely generalized regular fuzzy continuous functions in the sense of a.p. sostak&apos;s and ramadan is introduced. some interesting properties and characterizations of them are investigated. also, some applications to fuzzy compact spaces are established.

It is shown that when the underlying sigma model of bosonic string theory is written in terms of single-valued fields, which live in the covering space of the target space, Abelian T-duality survives lattice regularization of the world-sheet. The projection onto the target-space is implemented through a sum over cohomology, which bears resemblance to summing over topological sectors in Yang-Mil...

Let A be a geometric arrangement such that codim(x) ≥ 2 for every x ∈ A. We prove that, if the complement space M(A) is rationally hyperbolic, then there exists an injective map L(u, v) → π⋆(ΩM(A)) ⊗ Q.

We introduce the injective tensor products and the projective tensor products of ordered vector spaces with Archimedean order unit and study their functorial properties. The local characterization of a nuclear space is given.

from the moduli space Rg of (non-trivial) étale double coverings of curves of genus g to the moduli space Ag−1 of principally polarized abelian varieties of dimension g − 1, called the Prym map. It was shown independently by Friedman-Smith [10], Kanev [13], Welters [20] and Debarre [6], that prg is generically injective for g ≥ 7. On the other hand, Mumford showed in [16, p. 346], that the Prym...