Concerning the fixed point property for λ-dendroids
CONTENTS§ 1. Introduction....................................................................................................................................................................... 5§ 2. Preliminaries.................................................................................................................................................................... 6§ 3. Smoothness........................................................................................................................................................................
The notion of atomic mappings was introduced by R. D. Anderson in [1] to describe special decompositions of continua. Soon, atomic mappings turned out to be important tools in continuum theory. In particular, it can be seen in [2] and [5] that these maps are very helpful to construct some special, singular continua. Thus, the mappings have proved to be interesting by themselves, and several of their properties have been discovered, e.g. in [6], [7] and [9]. The reader is referred to Table II of...
In the first part of the paper behavior of conditions related to local connectivity at a point is discussed if the space is transformed under a mapping that is interior or open at the considered point of the domain. The second part of the paper deals with metric locally connected continua. They are characterized as continua for which the hyperspace of their nonempty closed subjects is homogeneous with respect to open mappings. A similar characterization for the hyperspace of subcontinua remains...
We construct examples of mappings and between locally connected continua such that and are near-homeomorphisms while is not, and is a near-homeomorphism, while and are not. Similar examples for refinable mappings are constructed.
AbstractLet a family S of spaces and a class F of mappings between members of S be given. For two spaces X and Y in S we define if there exists a surjection f ∈ F of X onto Y. We investigate the quasi-order in the family of dendrites, where F is one of the following classes of mappings: retractions, monotone, open, confluent or weakly confluent mappings. In particular, we investigate minimal and maximal elements, chains and antichains in the quasi-order , and characterize spaces which can be...
CONTENTS1. Introduction.......................................................52. Preliminaries ....................................................83. General properties .........................................114. Mappings onto fans........................................145. Mappings onto an arc.....................................206. A characterization of the top...........................277. Open mappings and their lightness................288. Inverse limits...................................................399....
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.
We investigate absolute retracts for hereditarily unicoherent continua, and also the continua that have the arc property of Kelley (i.e., the continua that satisfy both the property of Kelley and the arc approximation property). Among other results we prove that each absolute retract for hereditarily unicoherent continua (for tree-like continua, for λ-dendroids, for dendroids) has the arc property of Kelley.
The article contains no abstract
A Mazurkiewicz set is a subset of a plane with the property that each straight line intersects in exactly two points. We modify the original construction to obtain a Mazurkiewicz set which does not contain vertices of an equilateral triangle or a square. This answers some questions by L.D. Loveland and S.M. Loveland. We also use similar methods to construct a bounded noncompact, nonconnected generalized Mazurkiewicz set.
Page 1 Next