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
Some results on dimension theory: Universal spaces
Some theorems on invariance of infinite dimension under open and closed mappings
Spaces with fibered approximation property in dimension n
A metric space M is said to have the fibered approximation property in dimension n (briefly, M ∈ FAP(n)) if for any ɛ > 0, m ≥ 0 and any map g: m × n → M there exists a map g′: m × n → M such that g′ is ɛ-homotopic to g and dim g′ (z × n) ≤ n for all z ∈ m. The class of spaces having the FAP(n)-property is investigated in this paper. The main theorems are applied to obtain generalizations of some results due to Uspenskij [11] and Tuncali-Valov [10].
Spaces with increment of dimension n
Strong Cohomological Dimension
We characterize strong cohomological dimension of separable metric spaces in terms of extension of mappings. Using this characterization, we discuss the relation between strong cohomological dimension and (ordinal) cohomological dimension and give examples to clarify their gaps. We also show that if X is a separable metric ANR and G is a countable Abelian group. Hence for any separable metric ANR X.
Strongly metrizable spaces of large dimension each separable subspace of which is zero-dimensional
Subspace and addition theorems for extension and cohomological dimensions. A problem of Kuzminov