A spectral sequence for stratified spaces and configuration spaces of points

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

A -algebra SPECTRAL SEQUENCE FOR FUNCTION SPACES

1.1 The main result. Given a map f : K → L of pointed CW complexes, let homf (K,L) denote the pointed space of pointed maps K → L, with f as the base point. Recall that a Πalgebra is a (≥ 1)-graded group with an action of the primary homotopy operations (for example, for any pointed topological space M there is a homotopy Π-algebra π∗M = {πiM}i=1). Given a map t : X → Y of Π-algebras, let homt(...

A New Class of Banach Sequence Spaces

Controllability of kinematic control systems on stratified configuration spaces

This paper considers nonlinear kinematic controllability of a class of systems called stratified. Roughly speaking, such stratified systems have a configuration space which can be decomposed into submanifolds upon which the system has a different set of equations of motion. For such systems, then, considering controllability is difficult because of the discontinuous form of the equations of mot...

Surgery and stratified spaces

The past couple of decades has seen significant progress in the theory of stratified spaces through the application of controlled methods as well as through the applications of intersection homology. In this paper we will give a cursory introduction to this material, hopefully whetting your appetite to peruse more thorough accounts. In more detail, the contents of this paper are as follows: the...