Analytification, localization and homotopy epimorphisms

Equivariant Homotopy Epimorphisms, Homotopy Monomorphisms and Homotopy Equivalences

Localization and Completion in Homotopy Theory

Localization and Periodicity in Unstable Homotopy Theory

In this paper, we develop a hierarchy of natural localizations of spaces, called the vn-periodizations for n 2: 0, which may be used to expose and study periodic phenomena in unstable homotopy theory. These vn-periodizations act less radically than the corresponding homological localizations [2] and respect fibrations to a very considerable extent. A major part of this paper is devoted to devel...

Geometry of Epimorphisms and Frames

Using a bijection between the set BH of all Bessel sequences in a (separable) Hilbert space H and the space L(`2,H) of all (bounded linear) operators from `2 to H, we endow the set F of all frames in H with a natural topology for which we determine the connected components of F . We show that each component is a homogeneous space of the group GL(`2) of invertible operators of `2. This geometric...

Ring Epimorphisms and C(x)

This paper studies the homomorphism of rings of continuous functions ρ:C(X) → C(Y ), Y a subspace of a Tychonoff space X, induced by restriction. We ask when ρ is an epimorphism in the categorical sense. There are several appropriate categories: we look at CR, all commutative rings, and R/N, all reduced commutative rings. When X is first countable and perfectly normal (e.g., a metric space), ρ ...