The compactificability classes of certain spaces.
The compactificability classes: The behavior at infinity.
The compactness number of a compact topological space I
The compactness operator in general topology
The completion monad and its algebra
The Complex Stone-Weierstrass Property
The compact Hausdorff space X has the CSWP iff every subalgebra of C(X,ℂ) which separates points and contains the constant functions is dense in C(X,ℂ). Results of W. Rudin (1956) and Hoffman and Singer (1960) show that all scattered X have the CSWP and many non-scattered X fail the CSWP, but it was left open whether having the CSWP is just equivalent to being scattered. Here, we prove some general facts about the CSWP; in particular we show that if X is a compact ordered space,...
The complexity of the set of squares in the homeomorphism group of the circle
The set of squares in the group of autohomeomorphisms of the circle is complete analytic, and hence analytic but not Borel.
The complexity of -discretely decomposable families in uniform spaces
The concentration-compactness principle in the calculus of variations. The locally compact case, part 1
The concept of boundedness and the Bohr compactification of a MAP Abelian group
Let G be a maximally almost periodic (MAP) Abelian group and let ℬ be a boundedness on G in the sense of Vilenkin. We study the relations between ℬ and the Bohr topology of G for some well known groups with boundedness (G,ℬ). As an application, we prove that the Bohr topology of a topological group which is topologically isomorphic to the direct product of a locally convex space and an -group, contains “many” discrete C-embedded subsets which are C*-embedded in their Bohr compactification. This...
The concept of differential equation in topological spaces and generalized mechanics.
The congruences on S(X) which commute with V.
The Conley index for decompositions of isolated invariant sets
The Conley index for flows preserving generalized symmetries
Topological spaces with generalized symmetries are defined and extensions of the Conley index of a compact isolated invariant set of the flow preserving the structures introduced are proposed. One of the two new indexes is constructed with no additional assumption on the examined set in terms of symmetry invariance.
The connectedness of degeneracy loci
The connectedness of symmetric degeneracy loci: odd ranks. Appendix to "The connectedness of degeneracy loci" by L. W. Tu
The control agglomerations of an internet network with delay feedback.
The controlled separable projection property for Banach spaces
Let X, Y be two Banach spaces. We say that Y is a quasi-quotient of X if there is a continuous operator R: X → Y such that its range, R(X), is dense in Y. Let X be a nonseparable Banach space, and let U, W be closed subspaces of X and Y, respectively. We prove that if X has the Controlled Separable Projection Property (CSPP) (this is a weaker notion than the WCG property) and Y is a quasi-quotient of X, then the structure of Y resembles the structure of a separable Banach space: (a) Y/W is norm-separable...
The convergence approach to exponentiable maps.
The convergence of mean value iteration for a family of maps.