Characterization of Hilbert cube manifolds: an alternate proof
Characterizations of the countable infinite product of rationals and some related problems
Characterizations of uniformity-dependent dimension functions
Characterizing chainable, tree-like, and circle-like continua
We prove that a continuum X is tree-like (resp. circle-like, chainable) if and only if for each open cover 𝓤₄ = {U₁,U₂,U₃,U₄} of X there is a 𝓤₄-map f: X → Y onto a tree (resp. onto the circle, onto the interval). A continuum X is an acyclic curve if and only if for each open cover 𝓤₃ = {U₁,U₂,U₃} of X there is a 𝓤₃-map f: X → Y onto a tree (or the interval [0,1]).
Characterizing strong countable-dimensionality in terms of Baire category
Characterizing the arc by composition of functions
Characterizing the interval and circle by composition of functions
Circularity of graphs and continua: topology
Classical-type characterizations of non-metrizable ANE(n)-spaces
The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is (resp., ) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.
Classification of weakly infinite-dimensional spaces. Part II: Essential mappings
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.