‎For any archimedean$f$-ring $A$ with unit in whichbreak$awedge‎ ‎(1-a)leq 0$ for all $ain A$‎, ‎the following are shown to be‎ ‎equivalent‎: ‎ ‎1‎. ‎$A$ is isomorphic to the $l$-ring ${mathfrak Z}L$ of all‎ ‎integer-valued continuous functions on some frame $L$‎. 2‎. ‎$A$ is a homomorphic image of the $l$-ring $C_{Bbb Z}(X)$‎ ‎of all integer-valued continuous functions‎, ‎in the usual se...

Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_...

We prove the Existential Closedness conjecture for differential equation of j j -function and its derivatives. It states that in a differentia...

Let G G be a finitely presented group, and let H"> H encoding="application/x-tex">H subgroup of </inl...

‎for any archimedean$f$-ring $a$ with unit in whichbreak$awedge‎‎(1-a)leq 0$ for all $ain a$‎, ‎the following are shown to be‎‎equivalent‎:‎‎1‎. ‎$a$ is isomorphic to the $l$-ring ${mathfrak z}l$ of all‎‎integer-valued continuous functions on some frame $l$‎. 2‎. ‎$a$ is a homomorphic image of the $l$-ring $c_{bbb z}(x)$‎‎of all integer-valued continuous functions‎, ‎in the usual sense‎,‎on som...

In this paper, the concepts of LωH-sets and LωH-closed spaces are proposed in Lω-spaces by means of (αω)−-remote neighborhood family. The characterizations of LωH-sets and LωH-closed spaces are systematically discussed. Some important properties of LωH-closed spaces, such as the LωH-closed spaces is ω-regular closed hereditary, arbitrarily multiplicative and preserving invariance under almost (...

In this paper we investigate in which cases unions of identi$able classes are also necessarily identi$able. We consider identi$cation in the limit with bounds on mindchanges and anomalies. Though not closed under the set union, these identi$cation types still have features resembling closedness. For each of them we $nd n such that (1) if every union of n − 1 classes out of U1; : : : ; Un is ide...