Complexity of curves
We show that each of the classes of hereditarily locally connected, finitely Suslinian, and Suslinian continua is Π₁¹-complete, while the class of regular continua is Π₀⁴-complete.
Concerning a closed subset of a dendroid containing 2-ramification points
Concerning the structure of dendritic spaces
Conditions which ensure that a simple map does not raise dimension
The present paper deals with those continuous maps from compacta into metric spaces which assume each value at most twice. Such maps are called here, after Borsuk and Molski (1958) and as in our previous paper (1990), simple. We investigate the possibility of decomposing a simple map into essential and elementary factors, and the so-called splitting property of simple maps which raise dimension. The aim is to get insight into the structure of those compacta which have the property that simple maps...
Confluent mappings of fans [Book]
Connected CM-homomorphisms into semigroups of closed binary relations on hereditarily locally connected cont inua.
Containing spaces for planar rational compacta [Book]
Continua which a one-to-one continuous image of [0,∞)
Continua which admit no mean
A symmetric, idempotent, continuous binary operation on a space is called a mean. In this paper, we provide a criterion for the non-existence of mean on a certain class of continua which includes tree-like continua. This generalizes a result of Bell and Watson. We also prove that any hereditarily indecomposable circle-like continuum admits no mean.
Continua whose hyperspace is a product
Continua with the periodic-recurrent property.
Continuous decompositions of Peano plane continua into pseudo-arcs
Locally planar Peano continua admitting continuous decomposition into pseudo-arcs (into acyclic curves) are characterized as those with no local separating point. This extends the well-known result of Lewis and Walsh on a continuous decomposition of the plane into pseudo-arcs.
Continuous mappings on continua [Book]
Continuous monotone decompositions of planar curves
Continuous pseudo-hairy spaces and continuous pseudo-fans
A compact metric space X̃ is said to be a continuous pseudo-hairy space over a compact space X ⊂ X̃ provided there exists an open, monotone retraction such that all fibers are pseudo-arcs and any continuum in X̃ joining two different fibers of r intersects X. A continuum is called a continuous pseudo-fan of a compactum X if there are a point and a family ℱ of pseudo-arcs such that , any subcontinuum of intersecting two different elements of ℱ contains c, and ℱ is homeomorphic to X (with...
Curves which are continuous images of tree-like continua are movable
Dendrites and monotone mappings.
Dendritic decompositions of generalized simple closed curves
Dendroids and their endpoints
Ein eindimensionales Kompaktum in , das sich nicht lagetreu in die Mengersche Universalkurve einbetten läβt