On H. Priestley's dual of the category of bounded distributive lattices
On hereditarily decomposable hereditarily equivalent non-metric continua
On hereditarily indecomposable compacta
On hereditary interval algebras.
On homogeneous totally disconnected 1-dimensional spaces
The Cantor set and the set of irrational numbers are examples of 0-dimensional, totally disconnected, homogeneous spaces which admit elegant characterizations and which play a crucial role in analysis and dynamical systems. In this paper we will start the study of 1-dimensional, totally disconnected, homogeneous spaces. We will provide a characterization of such spaces and use it to show that many examples of such spaces which exist in the literature in various fields are all homeomorphic. In particular,...
On homotopically regular mappings of manifolds
On indecomposability and composants of chaotic continua
A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x,y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that . A homeomorphism f: X → X is continuum-wise expansive if there is c > 0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n ∈ ℤ such that . Clearly, every expansive homeomorphism is continuum-wise expansive, but the converse assertion is not true. In [6], we defined the notion of chaotic continua of homeomorphisms...
On indecomposable subcontinua of surfaces
On infinite words and dimension raising homomorphisms
On interior monotone mappings.
On internal composants of indecomposable plane continua
On irreducibility and indecomposability of continua
On lexicographic products
On local 1-connectedness of Whitney continua
On local expansions
On locally connected plane one-to-one continuous images of [0,∞)
On locally homeomorphic images of irreducible continua
On locally -incomparable families of infinite-dimensional Cantor manifolds
The notion of locally -incomparable families of compacta was introduced by K. Borsuk [KB]. In this paper we shall construct uncountable locally -incomparable families of different types of finite-dimensional Cantor manifolds.
On maps preserving connectedness and/or compactness
We call a function P-preserving if, for every subspace with property P, its image also has property P. Of course, all continuous maps are both compactness- and connectedness-preserving and the natural question about when the converse of this holds, i.e. under what conditions such a map is continuous, has a long history. Our main result is that any nontrivial product function, i.e. one having at least two nonconstant factors, that has connected domain, range, and is connectedness-preserving...
On Mazurkiewicz sets
A Mazurkiewicz set is a subset of a plane with the property that each straight line intersects in exactly two points. We modify the original construction to obtain a Mazurkiewicz set which does not contain vertices of an equilateral triangle or a square. This answers some questions by L.D. Loveland and S.M. Loveland. We also use similar methods to construct a bounded noncompact, nonconnected generalized Mazurkiewicz set.