The Sorgenfrey plane in dimension theory
The Sorgenfrey topology is a join of orderable topologies
The space of Whitney levels is homeomorphic to
The spaces of ordered lo-proximity
The span and the width of continua
The structure of atoms (hereditarily indecomposable continua)
Let X be an atom (= hereditarily indecomposable continuum). Define a metric ϱ on X by letting where is the (unique) minimal subcontinuum of X which contains x and y and W is a Whitney map on the set of subcontinua of X with W(X) = 1. We prove that ϱ is an ultrametric and the topology of (X,ϱ) is stronger than the original topology of X. The ϱ-closed balls C(x,r) = y ∈ X:ϱ ( x,y) ≤ r coincide with the subcontinua of X. (C(x,r) is the unique subcontinuum of X which contains x and has Whitney value...
The structure of compacta satisfying dim(X×X) < 2dimX
The superextension of the closed unit interval is homeomorphic to the Hilbert cube
The Suslinian number and other cardinal invariants of continua
By the Suslinian number Sln(X) of a continuum X we understand the smallest cardinal number κ such that X contains no disjoint family ℂ of non-degenerate subcontinua of size |ℂ| > κ. For a compact space X, Sln(X) is the smallest Suslinian number of a continuum which contains a homeomorphic copy of X. Our principal result asserts that each compact space X has weight ≤ Sln(X)⁺ and is the limit of an inverse well-ordered spectrum of length ≤ Sln(X)⁺, consisting of compacta with weight ≤ Sln(X) and...
The theorem of Miss Mullikin-Mazurkiewicz-van East for unicoherent Peano spaces
The topological fixed point property - an elementary continuum-theoretic approach
A set contained in a topological space has the topological fixed point property if every continuous mapping of the set into itself leaves some point fixed. In 1969, R. H. Bing published his article The Elusive Fixed Point Property, posing twelve intriguing and difficult problems, which exerted a great influence on the study of the fixed point property. We now present a survey article intended for a broad audience that reports on this area of fixed point theory. The exposition is also intended to...
The topological structure of planar closed spirals which support clans.
The topology of the unit interval is not uniquely determined by its continuous self maps among set systems
The Whitehead Theorem in the theory of shapes
There Are No Essential Phantom Mappings from 1-dimensional CW-complexes
A phantom mapping h from a space Z to a space Y is a mapping whose restrictions to compact subsets are homotopic to constant mappings. If the mapping h is not homotopic to a constant mapping, one speaks of an essential phantom mapping. The definition of (essential) phantom pairs of mappings is analogous. In the study of phantom mappings (phantom pairs of mappings), of primary interest is the case when Z and Y are CW-complexes. In a previous paper it was shown that there are no essential phantom...
Three countable connected spaces
Three questions of Borsuk concerning movability and fundamental retraction
Tietze's convexity theorey for lattices and semilattices.
Topological difference posets
Topological extensions and subspaces of -sets