A countable connected Urysohn space with a dispersion point that is regular almost everywhere
A counterexample in non-metric continua theory
A counter-example on unicoherent Peano spaces
A decomposition theorem for a class of continua for which the set function T is continuous
We prove a decomposition theorem for a class of continua for which F. B.. Jones's set function 𝓣 is continuous. This gives a partial answer to a question of D. Bellamy.
A decomposition theorem for collections of universal subcontinua
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 fixed point principle for locally expansive multifunctions
A fixed point theorem for continua which are hereditarily divisible by points
A fixed point theorem for plane homeomorphisms
A fixed-point anomaly in the plane
We define an unusual continuum M with the fixed-point property in the plane ℝ². There is a disk D in ℝ² such that M ∩ D is an arc and M ∪ D does not have the fixed-point property. This example answers a question of R. H. Bing. The continuum M is a countable union of arcs.
A formula for calculation of metric dimension of converging sequences
Converging sequences in metric space have Hausdorff dimension zero, but their metric dimension (limit capacity, entropy dimension, box-counting dimension, Hausdorff dimension, Kolmogorov dimension, Minkowski dimension, Bouligand dimension, respectively) can be positive. Dimensions of such sequences are calculated using a different approach for each type. In this paper, a rather simple formula for (lower, upper) metric dimension of any sequence given by a differentiable convex function, is derived....
A further discussion on Galambos problem.
A fuzzy modification of the category of linearly ordered spaces
A hereditarily indecomposable, hereditarily non-chainable planar tree-like continuum
A hereditarily indecomposable non-metric Hausdorff continuum
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