A spectral sequence approach to embedding spaces

A Spectral Sequence Approach to Normal Forms

Embedding Orlicz Sequence Spaces into C(α)

Let M be a non-degenerate Orlicz function such that there exist ǫ > 0 and 0 < s < 1 with ∑ ∞ i=1 M(ǫs)/M(s) < ∞. It is shown that the Orlicz sequence space hM is isomorphic to a subspace of C(ω). It is also shown that for any non-degenerate Orlicz function M , hM does not embed into C(α) for any α < ω .

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 Novel Approach to Embedding of Metric Spaces

An embedding of one metric space (X, d) into another (Y, ρ) is an injective map f : X → Y . The central genre of problems in the area of metric embedding is finding such maps in which the distances between points do not change “too much”. Metric Embedding plays an important role in a vast range of application areas such as computer vision, computational biology, machine learning, networking, st...

Embedding measure spaces

‎For a given measure space $(X,{mathscr B},mu)$ we construct all measure spaces $(Y,{mathscr C},lambda)$ in which $(X,{mathscr B},mu)$ is embeddable‎. ‎The construction is modeled on the ultrafilter construction of the Stone--v{C}ech compactification of a completely regular topological space‎. ‎Under certain conditions the construction simplifies‎. ‎Examples are given when this simplification o...