ANR's and NES's in the category of mappings on metric spaces
Aposyndesis in
We consider the Golomb and the Kirch topologies in the set of natural numbers. Among other results, we show that while with the Kirch topology every arithmetic progression is aposyndetic, in the Golomb topology only for those arithmetic progressions with the property that every prime number that divides also divides , it follows that being connected, being Brown, being totally Brown, and being aposyndetic are all equivalent. This characterizes the arithmetic progressions which are aposyndetic...
Application of covering sets
Application of fixed point theorem to best simultaneous approximation in convex metric spaces
Application on local discrete expansion.
...-Applications dans une variété
Applications of a mismatch, theorem to decomposition spaces
Applications of Brézis-Browder principle to the existence of fixed points and endpoint for multifunctions.
Applications of certain R-families
Applications of complete families of continuous functions to the theory of -spaces
Applications of fixed point theorems in the theory of generalized IFS.
Applications of limited information strategies in Menger's game
As shown by Telgársky and Scheepers, winning strategies in the Menger game characterize -compactness amongst metrizable spaces. This is improved by showing that winning Markov strategies in the Menger game characterize -compactness amongst regular spaces, and that winning strategies may be improved to winning Markov strategies in second-countable spaces. An investigation of 2-Markov strategies introduces a new topological property between -compact and Menger spaces.
Applications of Luzinian separation principles (non-separable case)
Applications of maximal μ-open sets in generalized topology and quasi topology
In this paper, some fundamental properties of maximal μ-open sets such as decomposition theorem for a maximal μ-open set, are given in a generalized topological space. Some basic properties of intersection of maximal μ-open sets are established, cohere the law of μ-radical μ-closure in a quasi topological space is obtained, among the other things.
Applications of some strong set-theoretic axioms to locally compact T₅ and hereditarily scwH spaces
Under some very strong set-theoretic hypotheses, hereditarily normal spaces (also referred to as T₅ spaces) that are locally compact and hereditarily collectionwise Hausdorff can have a highly simplified structure. This paper gives a structure theorem (Theorem 1) that applies to all such ω₁-compact spaces and another (Theorem 4) to all such spaces of Lindelöf number ≤ ℵ₁. It also introduces an axiom (Axiom F) on crowding of functions, with consequences (Theorem 3) for the crowding of countably compact...
Applications of the Baire-category method to the problem of independent sets
Applications of the Fréchet subdifferential
2000 Mathematics Subject Classification: 46A30, 54C60, 90C26.In this paper we prove two results of nonsmooth analysis involving the Fréchet subdifferential. One of these results provides a necessary optimality condition for an optimization problem which arise naturally from a class of wide studied problems. In the second result we establish a sufficient condition for the metric regularity of a set-valued map without continuity assumptions.
Applications of the Rådström-Hörmander Embedding Theorem to Multifunctions
Using the Rådström-Hörmander theorem on embedding of the hyperspace of closed convex sets in a Banach space, we prove multivalued versions of some results known for real functions.
Applications of the side approximation theorem for surfaces
Applications of topology to foundations of mathematics