pointwise compactness in spaces of continuous functions
... compact spaces, respectively, has become of great interest in the descriptive theory of Banach spaces and they have been studied by M. Talagrand [17], S. P. Gul'ko [10] and L. Vasak [20] among others. Nevertheless, as far as the author knows, given a K-analytic space X and an RNK subset A of CP(X), ...
... compact spaces, respectively, has become of great interest in the descriptive theory of Banach spaces and they have been studied by M. Talagrand [17], S. P. Gul'ko [10] and L. Vasak [20] among others. Nevertheless, as far as the author knows, given a K-analytic space X and an RNK subset A of CP(X), ...
Introduction to higher homotopy groups and
... to be different. A more restrictive definition requires the map to be a homeomorphism on each fiber. ...
... to be different. A more restrictive definition requires the map to be a homeomorphism on each fiber. ...
Anthony IRUDAYANATEIAN Generally a topology is
... Generally a topology is defined on any space by using some definition of “closeness” of points to subsets of that space. In particular, if F denotes the set of ail functions on a topological space X to a topological space Y, several definitions of closeness are known. For example, if x E X, f, g E F ...
... Generally a topology is defined on any space by using some definition of “closeness” of points to subsets of that space. In particular, if F denotes the set of ail functions on a topological space X to a topological space Y, several definitions of closeness are known. For example, if x E X, f, g E F ...
PDF
... nearness relation on X if it satisfies the following conditions: for A, B ∈ P (X), 1. if A ∩ B 6= ∅, then AδB; 2. if AδB, then A 6= ∅ and B 6= ∅; 3. (symmetry) if AδB, then BδA; 4. (A1 ∪ A2 )δB iff A1 δB or A2 δB; 5. Aδ 0 B implies the existence of C ⊆ X with Aδ 0 C and (X − C)δ 0 B, where Aδ 0 B me ...
... nearness relation on X if it satisfies the following conditions: for A, B ∈ P (X), 1. if A ∩ B 6= ∅, then AδB; 2. if AδB, then A 6= ∅ and B 6= ∅; 3. (symmetry) if AδB, then BδA; 4. (A1 ∪ A2 )δB iff A1 δB or A2 δB; 5. Aδ 0 B implies the existence of C ⊆ X with Aδ 0 C and (X − C)δ 0 B, where Aδ 0 B me ...
RESULT ON VARIATIONAL INEQUALITY PROBLEM 1
... [8] E. Zeidler, Nonlinear Functional Analysis and its Applications III, Variational methods and optimization, Translated from the German by Leo F. Boron, Springer-Verlag, ...
... [8] E. Zeidler, Nonlinear Functional Analysis and its Applications III, Variational methods and optimization, Translated from the German by Leo F. Boron, Springer-Verlag, ...
Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.Covering spaces play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. In Riemannian geometry for example, ramification is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the fundamental group. An important application comes from the result that, if X is a ""sufficiently good"" topological space, there is a bijection between the collection of all isomorphism classes of connected coverings of X and the conjugacy classes of subgroups of the fundamental group of X.