On symmetric products
On the 2-homogeneity of Cartesian products
On the additivity of the fixed point property for 1-dimensional continua
On the Baire order problem for a linear lattice of functions
On the classification of inverse limits of tent maps
Let and be tent maps on the unit interval. In this paper we give a new proof of the fact that if the critical points of and are periodic and the inverse limit spaces and are homeomorphic, then s = t. This theorem was first proved by Kailhofer. The new proof in this paper simplifies the proof of Kailhofer. Using the techniques of the paper we are also able to identify certain isotopies between homeomorphisms on the inverse limit space.
On the continua which are Cantor homogeneous or arcwise homogeneous
On the deficiency of product spaces
On the depth of a continuum
On the dimension modulo classes of topological spaces and free topological groups.
On the dimension of increments of Tychonoff spaces
On the dimension of ordered spaces.
On the dimension of remainders in extensions of product spaces
On the dimension of the space of ℝ-places of certain rational function fields
We prove that for every n ∈ ℕ the space M(K(x 1, …, x n) of ℝ-places of the field K(x 1, …, x n) of rational functions of n variables with coefficients in a totally Archimedean field K has the topological covering dimension dimM(K(x 1, …, x n)) ≤ n. For n = 2 the space M(K(x 1, x 2)) has covering and integral dimensions dimM(K(x 1, x 2)) = dimℤ M(K(x 1, x 2)) = 2 and the cohomological dimension dimG M(K(x 1, x 2)) = 1 for any Abelian 2-divisible coefficient group G.
On the disjoint (0,N)-cells property for homogeneous ANR's
A metric space (X,ϱ) satisfies the disjoint (0,n)-cells property provided for each point x ∈ X, any map f of the n-cell into X and for each ε > 0 there exist a point y ∈ X and a map such that ϱ(x,y) < ε, and . It is proved that each homogeneous locally compact ANR of dimension >2 has the disjoint (0,2)-cells property. If dimX = n > 0, X has the disjoint (0,n-1)-cells property and X is a locally compact -space then local homologies satisfy for k < n and Hn(X,X-x) ≠ 0.
On the division by Rn.
On the equivalence of certain coincidence theorems and fixed point theorems
On the existence of arcs in rational curves
On the existence of means on solenoids.
On the fundamental dimension of the Cartesian product of compacta with the fundamental dimension 2
On the Hausdorff Dimension of Topological Subspaces
It is shown that every Polish space X with admits a compact subspace Y such that where and denote the topological and Hausdorff dimensions, respectively.