On the continua which are Cantor homogeneous or arcwise homogeneous
On the depth of a continuum
On the existence of arcs in rational curves
On the existence of means on solenoids.
On the fundamental dimension of the Cartesian product of compacta with the fundamental dimension 2
On the homology of the Harmonic Archipelago
We calculate the singular homology and Čech cohomology groups of the Harmonic Archipelago. As a corollary, we prove that this space is not homotopy equivalent to the Griffiths space. This is interesting in view of Eda’s proof that the first singular homology groups of these spaces are isomorphic.
On the hyperspace
Let be a continuum and a positive integer. Let be the hyperspace of all nonempty closed subsets of with at most components, endowed with the Hausdorff metric. For compact subset of , define the hyperspace . In this paper, we consider the hyperspace , which can be a tool to study the space . We study this hyperspace in the class of finite graphs and in general, we prove some properties such as: aposyndesis, local connectedness, arcwise disconnectedness, and contractibility.
On the hyperspace of subcontinua of a finite graph I
On the hyperspace of subcontinua of a finite graph, II
On the hyperspaces of hereditarily indecomposable continua
On the hyperspaces of snake-like and circle-like continua
On the LC1-spaces which are Cantor or arcwise homogeneous
A space X containing a Cantor set (an arc) is Cantor (arcwise) homogeneousiff for any two Cantor sets (arcs) A,B ⊂ X there is an autohomeomorphism h of X such that h(A)=B. It is proved that a continuum (an arcwise connected continuum) X such that either dim X=1 or is Cantor (arcwise) homogeneous iff X is a closed manifold of dimension at most 2.
On the local homogeneity and the invertibility of a topological space
On the Maćkowiak-Tymchatyn theorem
On the planarity of Peano generalized continua: An extension of a theorem of S. Claytor
We extend a theorem of S. Claytor in order to characterize the Peano generalized continua which are embeddable into the 2-sphere. We also give a characterization of the Peano generalized continua which admit closed embeddings in the Euclidean plane.
On the rim-types of hereditarily locally connected continua
On the span of weakly-chainable continua
On the structure of the intersection of two middle third Cantor sets.
Motivated by the study of planar homoclinic bifurcations, in this paper we describe how the intersection of two middle third Cantor sets changes as the sets are translated across each other. The resulting description shows that the intersection is never empty; in fact, the intersection can be either finite or infinite in size. We show that when the intersection is finite then the number of points in the intersection will be either 2n or 3 · 2n. We also explore the Hausdorff dimension of the intersection...
On the structure of tranches in continuously irreducible continua
On the surjective span and semispan of connected metric spaces