Small retractions of smooth dendroids onto trees
Smooth dendroids as inverse limits of dendrites
Smooth dendroids without ordinary points
Smoothness and the property of Kelley
Interrelations between smoothness of a continuum at a point, pointwise smoothness, the property of Kelley at a point and local connectedness are studied in the paper.
Some characterizations of bitopological connectivity properties
Some curves of prescribed rim-types
Some facts about homogeneity properties
Some functions on hyperspaces of hereditarily unicoherent continua
Some local properties of Suslinian compacta
Some partitions consisting of Jordan curves.
Some problems concerning curves
Some union theorems for confluent mappings
Spaces of ANR's
Spaces of retractions which are homeomorphic to Hilbert space
Spaces of σ-finite linear measure
Spaces of finite n-dimensional Hausdorff measure are an important generalization of n-dimensional polyhedra. Continua of finite linear measure (also called continua of finite length) were first characterized by Eilenberg in 1938. It is well-known that the property of having finite linear measure is not preserved under finite unions of closed sets. Mauldin proved that if X is a compact metric space which is the union of finitely many closed sets each of which admits a σ-finite linear measure then...
Striped structures of stable and unstable sets of expansive homeomorphisms and a theorem of K. Kuratowski on independent sets
We investigate striped structures of stable and unstable sets of expansive homeomorphisms and continuum-wise expansive homeomorphisms. The following theorem is proved: if f : X → X is an expansive homeomorphism of a compact metric space X with dim X > 0, then the decompositions and of X into stable and unstable sets of f respectively are uncountable, and moreover there is σ (= s or u) and ϱ > 0 such that there is a Cantor set C in X with the property that for each x ∈ C, contains a nondegenerate...
Strongly cellular subsets of
Strongly chaotic dendrites
The concept of a strongly chaotic space is introduced, and its relations to chaotic, rigid and strongly rigid spaces are studied. Some sufficient as well as necessary conditions are shown for a dendrite to be strongly chaotic.
Strongly homotopically stabile points
Strongly metrizable spaces of large dimension each separable subspace of which is zero-dimensional