-movable and -calm compacta and their images
A characterization of movable compacta.
A characterization of strong inductive dimension
A class of infinite-dimensional spaces. Part I: Dimension theory and Alexandrof's problem
A class of infinite-dimensional spaces. Part II: An Extension Theorem and the theory of retracts
A condition equivalent to covering dimension for normal spaces
A connection between multiplication in C(X) and the dimension of X
Let X be a compact Hausdorff topological space. We show that multiplication in the algebra C(X) is open iff dim X < 1. On the other hand, the existence of non-empty open sets U,V ⊂ C(X) satisfying Int(U· V) = ∅ is equivalent to dim X > 1. The preimage of every set of the first category in C(X) under the multiplication map is of the first category in C(X) × C(X) iff dim X ≤ 1.
A dimension raising hereditary shape equivalence
We construct a hereditary shape equivalence that raises transfinite inductive dimension from ω to ω+1. This shows that ind and Ind do not admit a geometric characterisation in the spirit of Alexandroff's Essential Mapping Theorem, answering a question asked by R. Pol.
A dimensional property of Cartesian product
We show that the Cartesian product of three hereditarily infinite-dimensional compact metric spaces is never hereditarily infinite-dimensional. It is quite surprising that the proof of this fact (and this is the only proof known to the author) essentially relies on algebraic topology.
A factorization theorem for the transfinite kernel dimension of metrizable spaces
We prove a factorization theorem for transfinite kernel dimension in the class of metrizable spaces. Our result in conjunction with Pasynkov's technique implies the existence of a universal element in the class of metrizable spaces of given weight and transfinite kernel dimension, a result known from the work of Luxemburg and Olszewski.
A few remarks on blowing-up and connectedness.
A further discussion on Galambos problem.
A hereditarily normal strongly zero-dimensional space containing subspaces of arbitrarily large dimension
A hereditarily normal strongly zero-dimensional space with a subspace of positive dimension and an N-compact space of positive dimension
A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension
We give a non-probabilistic proof of a theorem of Naor and Neiman that asserts that if (E, d) is a doubling metric space, there is an integer N > 0, depending only on the metric doubling constant, such that for each exponent α ∈ (1/2; 1), one can find a bilipschitz mapping F = (E; dα ) ⃗ ℝ RN.
A non-zero dimensional atom in the lattice of uniformities
A note on dimension theory of metric spaces
A note on embeddings manifolds into topological groups preserving dimensions
A note on the dimension Dind
A note on transfinite dimension