Real-valued continuous functions and the span of continua
Recent research in hyperspace theory.
Regarding arc-wise accessibility in the plane
Remarks on some class of continuous mappings of λ-dendroids
Remarks on the absolute suspension
Removing sets from connected product spaces while preserving connectedness
As per the title, the nature of sets that can be removed from a product of more than one connected, arcwise connected, or point arcwise connected spaces while preserving the appropriate kind of connectedness is studied. This can depend on the cardinality of the set being removed or sometimes just on the cardinality of what is removed from one or two factor spaces. Sometimes it can depend on topological properties of the set being removed or its trace on various factor spaces. Some of the results...
Retral spaces and continua with the fixed point property
We show that every retral continuum with the fixed point property is locally connected. It follows that an indecomposable continuum with the fixed point property is not a retract of a topological group.
Semi-confluent and weakly confluent images of tree-like and atriodic continua
Semi-confluent mappings.
Semi-confluent mappings and their invariants
Semigroups on -spaces
Semigroups with only finitely many regular ... -classes.
Sets of end-points and ramification points in dendroids
Shadowing and expansivity in subspaces
We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.
Singular arc-like continua [Book]
Singular homology of n-cell-like continua
Size levels for arcs
We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.
Small retractions of smooth dendroids onto trees
Smooth dendroids as inverse limits of dendrites
Smooth dendroids without ordinary points