Addition and subspace theorems for asymptotic large inductive dimension
We prove the addition and subspace theorems for asymptotic large inductive dimension. We investigate a transfinite extension of this dimension and show that it is trivial.
Addition theorems and -spaces
It is proved that if a regular space is the union of a finite family of metrizable subspaces then is a -space in the sense of E. van Douwen. It follows that if a regular space of countable extent is the union of a finite collection of metrizable subspaces then is Lindelöf. The proofs are based on a principal result of this paper: every space with a point-countable base is a -space. Some other new results on the properties of spaces which are unions of a finite collection of nice subspaces...
Addition theorems, -spaces and dually discrete spaces
A neighbourhood assignment in a space is a family of open subsets of such that for any . A set is a kernel of if . If every neighbourhood assignment in has a closed and discrete (respectively, discrete) kernel, then is said to be a -space (respectively a dually discrete space). In this paper we show among other things that every GO-space is dually discrete, every subparacompact scattered space and every continuous image of a Lindelöf -space is a -space and we prove an addition...
Addition theorems for dense subspaces
We study topological spaces that can be represented as the union of a finite collection of dense metrizable subspaces. The assumption that the subspaces are dense in the union plays a crucial role below. In particular, Example 3.1 shows that a paracompact space which is the union of two dense metrizable subspaces need not be a -space. However, if a normal space is the union of a finite family of dense subspaces each of which is metrizable by a complete metric, then is also metrizable by...
Additional characterizations of the and weaker separation axioms
Additive properties and uniformly completely Ramsey sets
We prove some properties of uniformly completely Ramsey null sets (for example, every hereditarily Menger set is uniformly completely Ramsey null).
Additive selections of superadditive set-valued functions.
Additive set-functions in abstract spaces
Additive set-functions in abstract spaces.
Addresses
Adequate Compacta which are Gul’ko or Talagrand
2000 Mathematics Subject Classification: 54H05, 03E15, 46B26We answer positively a question raised by S. Argyros: Given any coanalytic, nonalytic subset Σ′ of the irrationals, we construct, in Mercourakis space c1(Σ′), an adequate compact which is Gul’ko and not Talagrand. Further, given any Borel, non Fσ subset Σ′ of the irrationals, we construct, in c1(Σ′), an adequate compact which is Talagrand and not Eberlein.Supported by grants AV CR 101-90-03, and GA CR 201-01-1198
Adequate families of sets and Corson compacts
Adequate families of sets and function spaces
Adjungiertenbildungen in der Operatortheorie.
Admissible maps, intersection results, coincidence theorems
We obtain generalizations of the Fan's matching theorem for an open (or closed) covering related to an admissible map. Each of these is restated as a KKM theorem. Finally, applications concerning coincidence theorems and section results are given.
Affine Flows and Distal Points.
Affine group acting on hyperspaces of compact convex subsets of ℝⁿ
For every n ≥ 2, let cc(ℝⁿ) denote the hyperspace of all nonempty compact convex subsets of the Euclidean space ℝⁿ endowed with the Hausdorff metric topology. Let cb(ℝⁿ) be the subset of cc(ℝⁿ) consisting of all compact convex bodies. In this paper we discover several fundamental properties of the natural action of the affine group Aff(n) on cb(ℝⁿ). We prove that the space E(n) of all n-dimensional ellipsoids is an Aff(n)-equivariant retract of cb(ℝⁿ). This is applied to show that cb(ℝⁿ) is homeomorphic...
Affine selections of convex set-valued functions.
a-inflatable semigroups.
Alcune caratterizzazioni di una sottoalgebra di e compattificazioni ad essa associate