Recognition of certain classes of closed maps
Recognizing approximate -tameness.
Recouvrements, derivation des mesures et dimensions.
Let X be a set with a symmetric kernel d (not necessarily a distance). The space (X,d) is said to have the weak (resp. strong) covering property of degree ≤ m [briefly prf(m) (resp. prF(m))], if, for each family B of closed balls of (X,d) with radii in a decreasing sequence (resp. with bounded radii), there is a subfamily, covering the center of each element of B, and of order ≤ m (resp. splitting into m disjoint families). Since Besicovitch, covering properties are known to be the main tool for...
Remarks on a conjecture of Hartshorne.
Remarks on characterization of dimension of separable metrizable spaces
Residuality of the set of embeddings into Nagata's n-dimensional universal spaces
Resolving a question of Arkhangel'skiĭ's
We construct in ZFC a cosmic space that, despite being the union of countably many metrizable subspaces, has covering dimension equal to 1 and inductive dimensions equal to 2.
Sätze aus der Functionentheorie
Semialgebraic Topology over a Real Closed Field II: Basic Theory of Semialgebraic Spaces.
Shape theory of maps.
We shall describe a modification of homotopy theory of maps which we call shape theory of maps. This is accomplished by constructing the shape category of maps HMb. The category HMb is built using multi-valued functions. Its objects are maps of topological spaces while its morphisms are homotopy classes of collections of pairs of multi-valued functions which we call multi-binets. Various authors have previously given other descriptions of shape categories of maps. Our description is intrinsic in...
Solution to a compactification problem of Sklyarenko
Some examples in the dimension theory of Tychonoff spaces
Some extension and classification theorems for maps of movable spaces
Some factorization theorems for paracompact -spaces
Some m-dimensional compacta admitting a dense set of imbeddings into
Some properties of fundamental dimension
Some properties of multiplication in the algebra related to the dimension of
Some properties of -dimensional generalized cubes
Some remarks concerning the fundamental dimension of the cartesian product of two compacta
Some remarks on subgroups of real numbers