Ob'edinenie i proizvedenie w - prostranstv
On 1/2-homogeneous ANR spaces
On a family of 2-dimensional AR-sets
On a generalization of absolute neighborhood retracts
On a method of constructing ANR-sets. An application of inverse limits
On a problem of Pełczyński: Milutin spaces, Dugundji spaces and AE(0-dim)
On a stability theorem for the fixed-point property
On absolute fixed-point sets
On absolute retracts, P(S) and complemented subspaces of
On barycentrically soft compacta
On bouquets
On Cartesian factors and the topological classification of linear metric spaces
On CE-images of the Hubert cube and characterization of Q-manifolds
On compactification of absolute retracts
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...