On the d-invariant of compact solvmanifolds.
Ordinals in topological groups
We show that if an uncountable regular cardinal τ and τ + 1 embed in a topological group G as closed subspaces then G is not normal. We also prove that an uncountable regular cardinal cannot be embedded in a torsion free Abelian group that is hereditarily normal. These results are corollaries to our main results about ordinals in topological groups. To state the main results, let τ be an uncountable regular cardinal and G a T₁ topological group. We prove, among others, the following statements:...
Propiedades topológicas de los grupos de isometría de un grupo reticulado.
This paper deals with the topological properties of groups of isometries of lattice-ordered groups and f-rings. The topologies considered are order-topology and the topology defined by null-sequences.
Sequential convergences on Boolean algebras defined by systems of maximal filters
We study sequential convergences defined on a Boolean algebra by systems of maximal filters. We describe the order properties of the system of all such convergences. We introduce the category of 2-generated convergence Boolean algebras and generalize the construction of Novák sequential envelope to such algebras.
Sur la caractérisation topologique des compacts à l'aide des demi-treillis des pseudométriques continues
For a Tikhonov space X we denote by Pc(X) the semilattice of all continuous pseudometrics on X. It is proved that compact Hausdorff spaces X and Y are homeomorphic if and only if there is a positive-homogeneous (or an additive) semi-lattice isomorphism T:Pc(X) → Pc(Y). A topology on Pc(X) is called admissible if it is intermediate between the compact-open and pointwise topologies on Pc(X). Another result states that Tikhonov spaces X and Y are homeomorphic if and only if there exists a positive-homogeneous...
Zero dimensional and connected domains.
Zero-dimensional Dugundji spaces admit profinite lattice structures
We prove what the title says. It then follows that zero-dimensional Dugundji space are supercompact. Moreover, their Boolean algebras of clopen subsets turn out to be semigroup algebras.
Внешние меры и внешние топологии
О секвенциальных порядковых топологиях.
Полные решетки конформно-инвариантных бикомпактных расширений.