On components of MANR-spaces
On continuous surjections from Cantor set.
It is a famous result of Alexandroff and Urysohn that every compact metric space is a continuous image of a Cantor set ∆. In this short note we complement this result by showing that a certain uniqueness property holds. Namely, if (K,d) is a compact metric space and f and g are two continuous mappings from ∆ onto K, the, for every e > 0 there exists a homeomorphism phi of ∆ such that d(g(x), f(phi(x))) < e for all x∆.
On fine shape theory II
On fundamental deformation retracts and on some related notions
On generalizations of Borsuk's homotopy extension theorem
On -bubbles in n-dimensional compacta
A topological space X is called an -bubble (n is a natural number, is Čech cohomology with integer coefficients) if its n-dimensional cohomology is nontrivial and the n-dimensional cohomology of every proper subspace is trivial. The main results of our paper are: (1) Any compact metrizable -bubble is locally connected; (2) There exists a 2-dimensional 2-acyclic compact metrizable ANR which does not contain any -bubbles; and (3) Every n-acyclic finite-dimensional -trivial metrizable compactum...
On interior monotone mappings.
On linear operators and functors extending pseudometrics
For some pairs (X,A), where X is a metrizable topological space and A its closed subset, continuous, linear (i.e., additive and positive-homogeneous) operators extending metrics for A to metrics for X are constructed. They are defined by explicit analytic formulas, and also regarded as functors between certain categories. An essential role is played by "squeezed cones" related to the classical cone construction. The main result: if A is a nondegenerate absolute neighborhood retract for metric spaces,...
On medial properties of maps
On movability and other similar shape properties
On movable compacta
On non compact FANR's and MANR's
On products of incompressible AR's
On properties preserved by the approximate domination
On rest points of dynamical systems
On shape
On some applications of infinite-dimensional manifolds to the theory of shape
On spaces which have the shape of compact metric spaces
On spaces with binary normal subbase
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.