On piecewise confluent mappings.
On self-homeomorphic dendrites
It is shown that for every numbers there is a strongly self-homeomorphic dendrite which is not pointwise self-homeomorphic. The set of all points at which the dendrite is pointwise self-homeomorphic is characterized. A general method of constructing a large family of dendrites with the same property is presented.
On some examples of monostratic λ-dendroids
On some test spaces in dimension theory
On span and chainable continua
On span and weakly chainable continua
On spirals and fixed point property
We study the famous examples of G. S. Young [7] and R. H. Bing [2]. We generalize and simplify a little their constructions. First we introduce Young spirals which play a basic role in all considerations. We give a construction of a Young spiral which does not have the fixed point property (see Section 5) . Then, using Young spirals, we define two classes of uniquely arcwise connected curves, called Young spaces and Bing spaces. These classes are analogous to the examples mentioned above. The definitions...
On the 2-homogeneity of Cartesian products
On the additivity of the fixed point property for 1-dimensional continua
On the depth of a continuum
On the division by Rn.
On the equivalence of certain coincidence theorems and fixed point theorems
On the Maćkowiak-Tymchatyn theorem
On the metric dimension of converging sequences
In the paper, some kind of independence between upper metric dimension and natural order of converging sequences is shown — for any sequence converging to zero there is a greater sequence with an arbitrary () upper dimension. On the other hand there is a relationship to summability of series — the set of elements of any positive summable series must have metric dimension less than or equal to .
On the shape of 0-dimensional paracompacta
On the topology of curves II
On the topology of curves III
On the topology of curves IV
On uncountable collections of continua and their span
We prove that if the Euclidean plane contains an uncountable collection of pairwise disjoint copies of a tree-like continuum X, then the symmetric span of X is zero, sX = 0. We also construct a modification of the Oversteegen-Tymchatyn example: for each ε > 0 there exists a tree such that σX < ε but X cannot be covered by any 1-chain. These are partial solutions of some well-known problems in continua theory.
On uniquely arcwise connected curves