A pro-C∗-algebra is a (projective) limit of C∗-algebras in the category of topological ∗algebras. From the perspective of non-commutative geometry, pro-C∗-algebras can be seen as non-commutative k-spaces. An element of a pro-C∗-algebra is bounded if there is a uniform bound for the norm of its images under any continuous ∗-homomorphism into a C∗-algebra. The ∗-subalgebra consisting of the bound...

The Congruence Lattice Problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of a lattice. It was hoped that a positive solution would follow from E. T. Schmidt’s construction or from the approach of P. Pudlák, M. Tischendorf, and J. Tůma. In a previous paper, we constructed a distributive algebraic lattice A with א2 compact elements that cannot be ob...

S U M M A R Y We present an alternative to the classical mode coupling method scheme often used in global seismology to compute synthetic seismograms in laterally heterogeneous earth model and Frechet derivatives for tomographic inverse problem with the normal modes first-order Born approximation. We start from the first-order Born solution in the frequency domain and we use a numerical scheme ...

It is shown that the metric on union of sets X and Y defines a Hilbert $C^*$ -module over uniform Roe algebra space with fixed dX. A number examples such -modules are described.

Description of the pairs 〈low approximation, upper approximation〉 of rough sets is an important aspect in the research of rough set theory by algebraic method. By defining some basic operators on the approximation pairs, rough algebras can be constructed. Then some general algebras can be selected to describe the pairs of rough sets. The most famous rough algebras are Rough Double Stone Algebra...

We prove that for every singular cardinal μ of cofinality ω, the complete Boolean algebra compPμ(μ) contains a complete subalgebra which is isomorphic to the collapse algebra CompCol(ω1, μ0 ). Consequently, adding a generic filter to the quotient algebra Pμ(μ) = P(μ)/[μ] collapses μ0 to א1. Another corollary is that the Baire number of the space U(μ) of all uniform ultrafilters over μ is equal ...