Weakly confluent mappings and a classification of continua
Some order theoretic characterizations of the 3-cell
Continua whose connected subsets are arcwise connected
Containing spaces for planar rational compacta
CONTENTS1. Introduction.............................................................................52. Ordered scattered spaces......................................................6 2.1. Topological type..................................................................6 2.2. Ordered spaces..................................................................6 2.3. Rim-type.............................................................................9 2.4. Disk partitions.....................................................................93....
Continuous mappings on continua II
CONTENTSIntroduction......................................................................................51. General notion of aposyndesis....................................................62. Relation T for special families......................................................83. Properties of T.............................................................................94. T-aposyndesis in homogeneous continua..................................115. Colocal connectedness and T-aposyndesis...............................136....
Universal rational spaces
CONTENTS1. Introduction......................................................................52. Rim-type and decompositions..........................................83. Defining sequences and isomorphisms..........................184. Embedding theorem.......................................................265. Construction of universal and containing spaces...........326. References....................................................................39
Some properties of open and related mappings
On hereditarily indecomposable compacta
Some classes of locally connected continua
Hereditarily σ-connected continua
The Menger curve Characterization and extension of homeomorphisms of non-locally-separating closed subsets
CONTENTS1. Introduction.................................................................................................................................................52. Partitioning Peano continua......................................................................................................................103. Peano continua and cross-connectedness...............................................................................................184. The characterization of the Menger curve.................................................................................................285....
On three problems of Franklin and Wallace concerning partially ordered spaces
Non-separating subcontinua of planar continua
We revisit an old question of Knaster by demonstrating that each non-degenerate plane hereditarily unicoherent continuum X contains a proper, non-degenerate subcontinuum which does not separate X.
On continuous extension of uniformly continuous functions and metrics
We prove that there exists a continuous regular, positive homogeneous extension operator for the family of all uniformly continuous bounded real-valued functions whose domains are closed subsets of a bounded metric space (X,d). In particular, this operator preserves Lipschitz functions. A similar result is obtained for partial metrics and ultrametrics.
Topology and measure of buried points in Julia sets
It is well-known that the set of buried points of a Julia set of a rational function (also called the residual Julia set) is topologically “fat” in the sense that it is a dense if it is non-empty. We show that it is, in many cases, a full-measure subset of the Julia set with respect to conformal measure and the measure of maximal entropy. We also address Hausdorff dimension of buried points in the same cases, and discuss connectivity and topological dimension of the set of buried points. Finally,...
Hereditarily indecomposable inverse limits of graphs
We prove the following theorem: Let G be a compact connected graph and let f: G → G be a piecewise linear surjection which satisfies the following condition: for each nondegenerate subcontinuum A of G, there is a positive integer n such that fⁿ(A) = G. Then, for each ε > 0, there is a map which is ε-close to f such that the inverse limit is hereditarily indecomposable.
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