We characterize the category of injective *-homomorphisms between commutative C*-subalgebras of various C*-algebras, namely C*-algebras of operators on separable Hilbert spaces, any finite-dimensional C*-algebra, and any commutative C*-algebra.

We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...

The present study investigates some novel categorical properties of soft sets. By combining categorical theory with soft set theory, a categorical framework of soft set theory is established. It is proved that the category SFun of soft sets and soft functions has equalizers, finite products, pullbacks, and exponential properties. It is worth mentioning that we find that SFun is both a topologic...

We study the category of graded finite-dimensional representations of the polynomial current algebra associated to a simple Lie algebra. We prove that the category has enough injectives and compute the graded character of the injective envelopes of the simple objects as well as extensions betweeen simple objects. The simple objects in the category are parametized by the affine weight lattice. W...

We prove the existence of globally injective weak solutions in mixed boundary-value problems of second-gradient nonlinear elastostatics via energy minimization. This entails the treatment of self-contact. In accordance with the classical (first-gradient) theory, the model incorporates the unbounded growth of the potential energy density as the local volume ratio approaches zero. We work in a cl...

We claim that monomorphisms in Sets and Groups are the usual injective maps and homomorphisms. First, suppose that f : A → B is a set injection and that fg = gh. Then for all c ∈ C, we have f(g(c)) = f(h(c)) implies g(c) = h(c) by injectivitiy. Hence g = h. Conversely, suppose f : A → B is not an injection. Then let f(a) = f(a′) for some a 6= a′ ∈ A. Then let g(c) = a and h(c) = a′ for all c ∈ ...

It is proved that localizations of injective R-modules of finite Goldie dimension are injective if R is an arithmetical ring satisfying the following condition: for every maximal ideal P , RP is either coherent or not semicoherent. If, in addition, each finitely generated R-module has finite Goldie dimension, then localizations of finitely injective R-modules are finitely injective too. Moreove...

1 Definitions An orbifold is a Hausdorff space X0 along with an open cover {Ui} that is closed under finite intersection with the following properties. For each Ui there is an open set Ũi ⊆ R and a finite group Γi which acts on Ũi. In addition there is a homeomorphism φi : Ui ≈ Ũi/Γi and whenever Ui ⊂ Uj there is an injective homomorphism fij : Γi ↪→ Γj and Ũi can be embedded in Ũj such that th...

This paper gives a proof that the universal cover of a closed 3-manifold built from three π1-injective handlebodies is homeomorphic to R. This construction is an extension to handlebodies of the conditions for gluing of three solid tori to produce non-Haken Seifert fibered manifolds with infinite fundamental group. This class of manifolds has been shown to contain non-Haken non-Seifert fibered ...

Let M be a closed oriented surface of genus g ≥ 1, let Bn(M) be the braid group of M on n strings, and let SBn(M) be the corresponding singular braid monoid. Our purpose in this paper is to prove that the desingularization map η : SBn(M) → Z[Bn(M)], introduced in the definition of the Vassiliev invariants (for braids on surfaces), is injective. AMS Subject Classification: Primary 20F36; Seconda...