Classification of weakly infinite-dimensional spaces. Part I: A transfinite extension of the covering dimension
Classifying stationary sets: a survey
Closed copies of the rationals
Closed mappings and local dimension
Closed subgroups in Banach spaces
We show that zero-dimensional nondiscrete closed subgroups do exist in Banach spaces E. This happens exactly when E contains an isomorphic copy of . Other results on subgroups of linear spaces are obtained.
Clumps of continua
Coarse dimensions and partitions of unity.
Gromov and Dranishnikov introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we investigate relationships between them generalizing results of Dranishnikov and Dranishnikov-Keesling-Uspienskij.
Cohomology, dimension and large Riemannian manifolds.
Colorings of Periodic Homeomorphisms
We calculate the exact value of the color number of a periodic homeomorphism without fixed points on a finite connected graph.
Combinatorial trees in Priestley spaces
We show that prohibiting a combinatorial tree in the Priestley duals determines an axiomatizable class of distributive lattices. On the other hand, prohibiting -crowns with does not. Given what is known about the diamond, this is another strong indication that this fact characterizes combinatorial trees. We also discuss varieties of 2-Heyting algebras in this context.
Common fixed point theorems in cone metric spaces.
Compact connected semilattices without the fixed point property.
Compact pospaces
Posets with property DINT which are compact pospaces with respect to the interval topologies are characterized.
Compact spaces homeomorphic to a ray of ordinals
Compact spaces that do not map onto finite products
We provide examples of nonseparable compact spaces with the property that any continuous image which is homeomorphic to a finite product of spaces has a maximal prescribed number of nonseparable factors.
Compacta which are quasi-homeomorphic with a disk
Compacta with the shape finite complexes
Compactification of pointed 1-movable spaces
Compactifications of ℕ and Polishable subgroups of
We study homeomorphism groups of metrizable compactifications of ℕ. All of those groups can be represented as almost zero-dimensional Polishable subgroups of the group . As a corollary, we show that all Polish groups are continuous homomorphic images of almost zero-dimensional Polishable subgroups of . We prove a sufficient condition for these groups to be one-dimensional and also study their descriptive complexity. In the last section we associate with every Polishable ideal on ℕ a certain Polishable...
Compactifications of partially ordered sets