相关论文: Topological density of ccc Boolean algebras - ever…

Let $G$ be an infinite compact group. We prove that for every cardinal $\kappa$ between the density and the weight of $G$, there exists a dense subgroup of $G$ of density $\kappa$.

A usual dichotomy is that in many cases, reasonably definable sets, satisfy the CH, i.e. if they are uncountable they have cardinality continuum. A strong dichotomy is when: if the cardinality is infinite it is continuum as in [Sh:273]. We…

The Boolean algebra of regular closed sets is prominent in topology, particularly as a dual for the Stone-Cech compactification. This algebra is also central for the theory of geometric computation, as a representation for combinatorial…

Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial…

We prove that for k an uncountable cardinal, there exist 2^k many non homeomorphic weakly compact convex subsets of weight k in the Hilbert space of density k.

Given a Boolean algebra $A$, we construct another Boolean algebra $B$ with no uncountable well-ordered chains such that the Banach space of real valued continuous functions $C(K_A)$ embeds isometrically into $C(K_B)$, where $K_A$ and $K_B$…

Extending a result of the first author and Katsura, we prove that for every UHF algebra $A$ of infinite type, in every uncountable cardinality $\kappa$ there are $2^\kappa$ nonisomorphic approximately matricial C*-algebras with the same…

We construct a J\'{o}nsson algebra of cardinality $\omega_1$ in the variety of J\'{o}nsson-Tarski algebras.

Extending a result of R. de la Vega, we prove that an infinite homogeneous compactum has cardinality $\mathfrak{c}$ if either it is the union of countably many dense or finitely many arbitrary countably tight subspaces. The question if…

A topological space $X$ is $strongly$ $rigid$ if each non-constant continuous map $f:X\to X$ is the identity map of $X$. A Hausdorff topological space $X$ is called $Brown$ if for any nonempty open sets $U,V\subseteq X$ the intersection…

We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…

Every $\mathrm{C}^*$-algebra, regardless of its density character, can be embedded into the Calkin algebra in a forcing extension of the universe obtained without collapsing any cardinal.

We classify all division algebras that are principal Albert isotopes of a cyclic Galois field extension of degree $n>2$ up to isomorphisms. We achieve a ``tight'' classification when the cyclic Galois field extension is cubic. The…

We demonstrate how virtually all common cardinal invariants associated to a von Neumann algebra M can be computed from the decomposability number, dec(M), and the minimal cardinality of a generating set, gen(M). Applications include the…

Under the assumption that the continuum c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(N)/fin has under CH and in the aleph2-Cohen…

Under $\mathfrak{p} = \mathfrak{c}$, we answer Question 24 of \cite{dikranjan&shakhmatov3} for cardinality ${\mathfrak c}$ , by showing that if a non-torsion Abelian group of size continuum admits a countably compact Hausdorff group…

Assuming the existence of a supercompact cardinal and an inaccessible above it, we construct a model of ZFC, in which all uncountable regular cardinals are inaccessible in HOD.

The concepts of a conditional set, a conditional inclusion relation and a conditional Cartesian product are introduced. The resulting conditional set theory is sufficiently rich in order to construct a conditional topology, a conditional…

We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…

A subset $\mathcal X$ of a C*-algebra $\mathcal A$ is called irredundant if no $A\in \mathcal X$ belongs to the C*-subalgebra of $\mathcal A$ generated by $\mathcal X\setminus \{A\}$. Separable C*-algebras cannot have uncountable…