-spaces and the Wallman compactification.
Terminal continua and the homogeneity
The box-counting dimension of the sine-curve
The classification of circle-like continua that admit expansive homeomorphisms
A homeomorphism h: X → X of a compactum X is expansive provided that for some fixed c > 0 and every x, y ∈ X (x ≠ y) there exists an integer n, dependent only on x and y, such that d(hⁿ(x),hⁿ(y)) > c. It is shown that if X is a solenoid that admits an expansive homeomorphism, then X is homeomorphic to a regular solenoid. It can then be concluded that a circle-like continuum admits an expansive homeomorphism if and only if it is homeomorphic to a regular solenoid.
The covering dimension of product of generalized Sorgenfrey lines
The dimension of analytic sets
The dimension of hyperspaces of non-metrizable continua
We prove that, for any Hausdorff continuum X, if dim X ≥ 2 then the hyperspace C(X) of subcontinua of X is not a C-space; if dim X = 1 and X is hereditarily indecomposable then either dim C(X) = 2 or C(X) is not a C-space. This generalizes some results known for metric continua.
The dimension of metrizable subspaces of Eberlein compacta and Eberlein compactifications of metrizable spaces
We prove that every Baire subspace Y of c₀(Γ) has a dense metrizable subspace X with dim X ≤ dim Y. We also prove that the Kimura-Morishita Eberlein compactifications of metrizable spaces preserve large inductive dimension. The proofs rely on new and old results concerning the dimension of uniform spaces.
The dimension of products of complete separable metric spaces
The dimension of remainders of rim-compact spaces
Answering a question of Isbell we show that there exists a rim-compact space X such that every compactification Y of X has dim(Y)≥ 1.
The Dimension of the Set of All Finite Subsets of the Continuum
The dimension of X^n where X is a separable metric space
For a separable metric space X, we consider possibilities for the sequence where . In Section 1, a general method for producing examples is given which can be used to realize many of the possible sequences. For example, there is such that , , for n >1, such that , and Z such that S(Z) = 4, 4, 6, 6, 7, 8, 9,.... In Section 2, a subset X of is shown to exist which satisfies and .
The Dimension Print of Most Convex Surfaces.
The disjoint arcs property for homogeneous curves
The local structure of homogeneous continua (curves) is studied. Components of open subsets of each homogeneous curve which is not a solenoid have the disjoint arcs property. If the curve is aposyndetic, then the components are nonplanar. A new characterization of solenoids is formulated: a continuum is a solenoid if and only if it is homogeneous, contains no terminal nontrivial subcontinua and small subcontinua are not ∞-ods.
The duality between lattice-ordered monoids and ordered topological spaces.
The equality of dimensions
The existence of local homeomorphisms of degree on local dendrites
In this paper we characterize local dendrites which are the images of themselves under local homeomorphisms of degree for each positive integer .
The factorization theorem for paracompact -spaces
The fixed point property for set-valued mappings
The fixed point property for set-valued mappings of some acyclic curves